I will have to go back and see what the Church as pointing to back then, but IIRC, there were a half a dozen or so passages that they pointed to, along with the theological implications [edit: some of the verses are cited by a modern geocentrist below]. Two points to keep in mind in the meantime:
1. The Bible does NOT teach, or insist upon, geocentrism. It was the Church that interpreted it this way, based on what they believed was a "plain and obvious" reading of the texts.
2. The point of controversy did not center around whether the earth was at the center of the entire universe, it never even got that far. What heliocentrism was telling them was that the earth was not even the center of our own solar system! It was just one of a number of planets orbiting around the sun. This seemed to the Church at the time as directly contradicting the Creation story. God created the earth first, then the sun and moon. So, how could the earth just be a satellite of the Sun? The same for the stars, they were put there to be a light for the earth. The earth was the star of the show, the centerpiece for which all heavenly bodies were made.
Viewed from their position, setting aside our current knowledge, you can see where they were coming from. In fact, there are still geocentrists to this day. They think that all the evidence for heliocentrism is just the result of agnostic and atheistic scientists trying to discredit the Scriptural account of creation. They believe all of you that accept these scientific theories of heliocentrism are just compromising Christians giving in to the worldly pressures, etc, etc. Sound familiar?
Here is an article written by a Christian astrophysicist who points out that there are still some Creationists who cling to geocentrism. I include this so that you can see that not only did the Church in the renaissance believe the Bible taught geocentrism, there are still some stubborn Christians who still do!
http://www.ibri.org/Tracts/geocntct.htm
He concludes as follows with words of reassurance to his listeners that geocentrism is not true and it is not taught by the Bible. What is important about this is that the author felt the need to write the article in the first place!
"These evidences indicate that there is no validity to the idea that the earth is the physical center of the universe. We as Christians have good reason to believe that the earth has a central place in God's redemptive plan, but it does not follow from this that our
location is central. God warned the nation of Israel not to think that because He had chosen them they were particularly great in themselves. The situation here is similar.
But what about those passages in Scripture which seem to indicate that the earth is standing still? The strongest passages of this sort are those that speak of the sun rising, or the sun and moon standing still at Joshua's command. None of these provide any support for the recent form of geocentrism in which the earth rotates but does not move through space. All of these passages are being
misinterpreted when we read them to mean that the earth cannot be going around the sun. The Bible writers are speaking from a reference frame located at some point on the surface of the earth, and this is exactly the case with modern astronomers when they speak of the time of
sunrise at Philadelphia. We no more need to fear that the One who inspired Scripture is making a mistake in the one case than are the astronomers in the other."
Here is a quote from a modern geocentrist "organization":
"Since, as previously stated, theology is true science (Gods science), then only through theological sources can one be absolutely sure of answers. Also, scientifically speaking, how can anyone go outside the universe to observe what is actually happening? Since this is impossible, God has provided us with an unerring source of truth. The Holy Scriptures, certainly a primary source, are absolutely geocentric. There are a number of passages to support the earth-centered reality. Refer, for example, to Genesis and the Psalms. Note
Psalms 18:5-6, 92:1, 95:10; also,
Ecclesiastes 1:4-6 and Josues long day (
Josue 10). Believe the truth revealed in perpetuity, when you read
Psalm 103, which anticipates Copernicus, Galileo and Einstein, and all the other innovators: the earth
"shall not be moved
forever and ever". (emphasis added)"
the site is here:
http://home.cfl.rr.com/rinaldo/hoax.htm
In the United States there is a society that defends Bible-based geocentrism, called the Association for Biblical Astronomy (founded in 1971 under the name of "The Tychonian Society"). The Association for Biblical Astronomy publishes a journal and books, and is led by a young-earth creationist who has a doctorate in astronomy from Case-Western Reserve University, Dr. Gerardus Bouw. Outside the U.S., in France and Belgium, a Catholic group called Cercle Scientifique et Historique, includes some members who support geocentrism.
Now, most of the creationist organizations have disavowed geocentrism, but I recall there was a controversy at either ICR or AIG when they made this official because some of their staunch members were geocentrists.