Further, I'm not sure why you want to single out the "American slave trade"? According to the Bible, this can also be justified. You may want to read what the Bible actually says
OK, I intend to cover the American Slave Trade from beginning to end and then see what the Bible says about this. I'm going by 'popular' perception here and may actually be wrong about what was going on.
0) Preliminaries: At the heart of the covenant between the nation of Israel and YHWH is the Ten Commandments. Not wanting to go through all of those, lets start with the summary of these that was commonly known during the first century: "Love the Lord your god with all your heart, with all your soul, with all your strength and with all your mind, and love your neighbour as yourself" (Luke 10:27, Matthew 22:37-39 from Deuteronomy 6:5 & Leviticus 19:18).
'Love' used here and pretty much throughout the New Testament is Agape Love - i.e. an act, rather than an emotion. Israelites should love YHWH and loving him means not doing things that dishonour him or hurt him or his goals. I similar thing could be said of loving your neighbour - doing one's best to help and not hinder your neighbour.
'Neighbour' as Christians define it is anyone in need (cf, the Good Samaritan in Luke 10, which Jesus uses as an example to show that our neighbour is anyone who needs our love). By implication this use of neighbour would be how God originally intended it to be used. Note that this is not some kind of blindness, like letting a serial killer go free because you love them. If you love your neighbour - you love all of them and that means measures to prevent one 'neighbour' from hurting another. This can be seen in the Torah laws where murder is punishable by death.
Israel had a purpose (as did pretty much all the Canaanite tribes): to bless all of the world (Genesis 12:1-3 & note that those who reciprocated the blessing would be blessed and those who did not would be cursed). Now it is clear that oppressing someone isn't going to be much of blessing to them.
Summary: The heart of the Law, is applicable to both Israelite and Christian equally, is to love God and then to love other human beings (and any reading of the New Testament shows that this is extended beyond its original Jewish framework).
1) Capture/Kidnap of Africans to be sold as slaves: Mostly this was conducted by Africans against Africans, though apparently Europeans also engaged in such practices, such was the lucrative nature of the slave trade.
Where Africans were capturing and kidnapping other Africans, they were probably not Christian as Christianity had been big on the east Coast (e.g. Ethiopia), but it is not certain how far it spread across Africa at this time.
Torah allows for capture of slaves during war, but only if the place being besieged surrender peacefully (Dt 20:10-15). Apart from the Promised Land Israel should only have been warring in defence of their land, which is why they are to leave the the cities behind (though destroyed) and return home. None of their military victories except for Canaan were about gaining land.
Christians on the other hand perceive the Kingdom of God to be not of this world and therefore would not be conquering other lands (didn't stop them doing it sadly, e.g. Crusades).
The reality of the few instances of direct capture by Europeans suggests that their motivation was pure greed - fill out their ships with slaves to be traded.
Conclusion: The Bible doesn't prohibit this, though it does not encourage it except in defensive war, which this wasn't.
2) Purchase of Slaves: This was the most common method that Europeans used to gain slaves - exchanging "guns, ammunition, alcohol,
Indigo died Indian textiles, and other factory-made goods." (Wikipedia) for slaves.
Personally I find this abhorrent, particularly as I know how the slaves were then treated, but the fact is that this practice is allowed in Torah - Leviticus 25:44. The Christian nations had stamped this out over a thousand years earlier leading to the rise of serfs rather than slaves, which may or may not have been just as badly managed (particularly from the 17th century onwards - e.g. French & Russian Revolutions).
I seem to recall that one of the Roman writers of the second century complained that Christians were buying slaves and setting them free. Whether all were set free is not clear, but the book of Philemon hints that Paul wanted Philemon to be freed to help in the ministry, though he is not compelled to do so. If slaves could do a better job of furthering the kingdom of God when they were free than when they remained in slavery it is possible that Christians would have done that.
Conclusion: This practise is allowed for in the Torah, and early Christians probably engaged in it before slavery was gradually phased out at the encouragement of Christians.
3) Transportation of Slaves: There is nothing in the bible about slaves being transported anywhere. However given that the most likely ways of obtaining slaves like this were from the surrounding nations, whether by capture or purchase, they would have been transported - possibly en masse if a city was captured. However the purpose of slaves was to work for their masters - something they couldn't do if dead. Both the Israelite Law and Christian Agape love would not accept the mistreatment of property.
The Slave Triangle transported human beings in an inhuman way. There is no getting around this. Watch a series like Roots or movies like Amistad and Amazing Grace as well as even a cursory research of the subject shows that the traders had absolutely no regard for the lives of those in their care. The loss of life was so bad that they would cram as many as possible like sardines on the ship and throw any dead or dying overboard. it is likely that the overcrowding was in fact a major reason for the sheer number of deaths.
On top of this there are cases where slavers threw all their living slaves overboard in order to claim on the insurance. Greed again trumping any kind of Christian love.
Women were often raped and when 'finished with' just thrown overboard. There is no justification for this in the Torah where rape is punishable by death and in Christianity where any kind of sexual deviancy is forbidden.
Conclusion: There can be no justification for the way that the slaves were treated on their journey across The Atlantic. There is no Biblical precedent in either New or Old Testament and had the slaves and slavers been Hebrews there would be grounds for multiple executions of traders (Ex 21:20, Lev 19:20, Lev 24:17; Lev 25:43)
4) Slavery on the Plantations: A large proportion of those who had ended up as slaves on the plantations became Christians. There are clear instances of plantation owners treating their slaves well and educating them and treating them like other workers. But there are plenty of instances where they were treated terribly, whether they were Christian or not.
Whippings and beatings appear to be routine. There may have been cases where some kind of punishment was justified, but the problem appears to be that such beatings occurred at the whim of the owner and with no kind of restitution for the victims as per the Torah (Ex 21:26, Dt 15:13). The New Testament expressly says that Masters should not threaten their slaves with no indication that this only applies to some elite group (Ephesians 6:9, also Colossians 4:1).
It does seem that murder was fairly common, although there were some prosecutions even early on in the colonies, though this seems to change. Hebrews wouldn't have treated any of their slaves in this way. Not just because murder was punishable by death, regardless of their status (e.g. Lev 24:17) but doing so meant that you had one less worker to work your fields, so it didn't make economic sense. I may be wrong, but I get the impression that plantation owners were mega rich and could just buy more slaves if they died. This kind of easy-come-easy-go attitude seems to have bled over into groups like the Ku-Klux-Klan. This method of treating people as property is neither endorsed nor encouraged anywhere in the Bible, with verses giving slaves any kind of value indicating that they had value to the master, not that they were 'owned'
While some owners did allow their slaves to gain freedom, the general impression given is that many did not, again contrary to Torah (Resident Foreigners were to be treated in the same as Hebrews, by extension then, Christian slaves should have been treated in the same way as Hebrew slaves - Leviticus 19:24). There is little or no indication of Sabbath Laws, nor of anyone Judging impartially in any situation.
Forced marriages were normal. There is precedent for this in Torah, though not in the way it actually seems to have been applied in many cases, though in Torah this would be considered 'arranged' and is likely to have been a much more amenable arrangement, particularly as many of the stronger slaves were treated like studs!
Rape was common also and clearly there is no precedent for this in Torah (see above section on the journey).
There is no indication anywhere that Sabbath freedom as depicted in the Torah was ever applied. Nor is there much indication that slaves earned money in order to gain their own freedom as was the situation in Jesus' time and to which Paul is referring in Ephesians/Colossians/Philemon. Some slaves gained freedom eventually by purchasing it, but again the trend seems to be against any kind of freedom from slavery.
Children of slaves were automatically slaves and put to work as soon as they were able - certainly not how Israelites would have treated their slave children, whether Hebrew or non-Hebrew. Nor does this seem to fit with Jesus's actions or words about the treatment of children (blessed).
Slaves were often prevented from being educated and a slave in the plantations who could read was a bad thing. Nevertheless slaves learned to read and the most common reading material available was the Bible, so it is not surprising that many turned to Christianity. It is such an embarrassment that African slaves were better at being Christ-like than white Europeans!
Conclusion: There is no precedent anywhere for rape or murder or torture and none for life-long slavery or preventing their eventual freedom. Nothing in the way that slaves were treated in America appears to have any basis is in the Bible and I suspect that if the so-called Christian owners were truthfully loving both God and their neighbour as Jesus tells them to, then many of them would have become horrified at their actions and the likely consequences for their eternal souls (consider John Newton as an example of someone who did eventually see the error of his ways).
Summary: Based on my limited research over the last couple of weeks, I would say that a case can be made for slavery in Christianity, but it would not bear resemblance to anything that we have seen above. Slaves would be captured in defensive wars (which one hopes would not be a common occurrence) or sold by non Christians to Christian Masters. Once they were slaves, the master was expected to look after his slaves and treat them fairly - in other words like they treated anyone else with the simple exception that they had been compelled to work for their master. There is no direct imperative as Christians to free slaves, unless they are applying Torah, in which case they should have a Sabbath year, but without that it wasn't necessary... but although the law wasn't considered binding for non-Jews (see Romans, Galatians), it was indicative and Christian masters should then always be thinking about training their slaves for self-sufficiency and letting them out into the world when they are ready - anything that would help further the kingdom of God. If the slave trade had occurred under Christian terms, it would have been a minor blip in history. Instead greedy profiteers from beginning to end turned something bad into something terrible. There is no justification whatsoever for the horrible actions of slave traders and slave owners.
The only thing that Torah can be used to support is the purchase of slaves from foreign nations, the rest is prohibited or punished or discouraged (which those in the Slave Triangle and Antebellum South seem to have conveniently ignored or removed from the Bibles they used).
So the American slave trade CANNOT be justified from the Bible. You should read it, ALL OF IT, and you would see that what happened in the 300 years of Atlantic slaving bears little or no resemblance to any form of slavery or servitude mentioned in the Bible.