Being a character witness for someone is not a problem if you stick to ONLY what you know about the person from your personal experience with him, and if you ONLY tell the truth about this personal experience and, mostly, if you are TOTALLY COMFORTABLE with the idea of supporting him and his bid for custody.
As a character witness, you should be careful not to make any false assumptions, offer up any false facts, deviate from the truth of what you know. You CANNOT say that he is a good person or a good father, for instance, because those are generalizations that may or may not be true all the time. You CAN relate tales about those times that you have seen him interact with his son and with others - experiences that can indicate that he is a good person and a good father.
Be honest and upfront with the father and let him know the limits of what you can honestly say. If you only see him briefly one hour a day, that is all you can testify to. If there is anything you may be asked to say that can be detrimental to his quest to gain custody, let him know that. The opposing party may work hard to get you to say something negative. If there IS a negative, tell him now.
Also be aware that the face a person presents to the public can be totally different than their face in private. You may hear horrible things about him from the boy's mother or her witnesses. If you have difficulty with that thought, especially knowing that you will have to continue to work with him and his son, you may want to decline the offer to be a character witness.
I cannot see that the church would be held liable for anything. It might be wise to ask if they have a problem with you being a character witness for one of their volunteers, however.