Are the Gospels the only sources of Christian morals?
The Gospels give us the direct words of the Lord himself, and so they are naturally the best direct witness to what he said. Leading on from them we have Acts and the letters of Paul, James, Peter etc, reflecting on those teachings, but always referring back to Christ himself.
Therefore, the ultimate source of Christian morality is always Christ and what he said. There is very good evidence to show that his words were collected both during his life and within 20 years of his death and resurrection. These collections of sayings in turn became the basis for the gospels. Therefore, of all the writing in the Bible, the words of Christ are regarded as among the most trustworthy, and they therefore form the basis for Christian morality and faith. Whatever any other apostle says has to be read through the words of Christ, and measured against them.
Some Bibles have the words of Christ printed in red; that would be a very useful way for a non Christian to determine this particular part of our Scripture.
I think you made the comment elsewhere about Christians choosing what to believe and what not to believe. This may well relate to the letters of Paul etc, which are open to interpretation and context. Paul is accepted as human, and fallible, as are all the other apostles, and there is then debate about how much God would influence his writing towards infallibility, and how much he would allow it to remain Paul's words. That debate goes on, because the Bible does not anywhere claim to be infallible; the best it says is that all Scripture is useful for teaching, and is inspired by God. (Timothy)
The words of Christ are far less disputed, because Christ himself was without sin, and his words are not open to the same possibility of fallibility. The morality which Christ himself establishes for Christians goes far beyond Jewish moral standards, and is very challenging indeed. He forbids divorce except for adultery, he says that being angry with our brother is just as much a sin as murder is, and he asks that we love our enemies and do good to those who hurt us; a lot of this must already be familliar to you.
Imo, anyone, Christian or not, who seriously considered the words of Christ himself would find that they represent a very real moral challenge. Christians accept that without God's help we are incapable of meeting this challenge, and that any ability we have to behave in a way which pleases God must first come from God. This gift of God to enable us to live in accordance with his will we call Grace, and it comes to us through the spirit of God, which is the Holy Spirit.
All Christians have the Holy Spirit living within them, which is the Spirit of Christ. Whenever we pray, it is the Holy Spirit which prompts us to do so. Ditto going to church or any other act of devotion or of love for our neighbours. We can do nothing without the Spirit of God.
