Hi W.,
I'm Catholic and my husband is not. We had our daughter baptized at St. Cornelius Church on the corner of Bellflower and Wardlow. Some of the other Catholic churches in the area were abrupt when I called and they wouldn't do it if we weren't already a member of the parish; St. Cornelius was accomodating. The Catholic Church requires that one of the godparents be Catholic, but the parish doesn't require you to provide any proof that they are - it's up to your conscience :-). They want the parents to take an education class (with a $50 recommended donation to the Church) prior to scheduling the baptism, and they also ask that the godparents take the class. I scheduled the baptism in a rush because I wanted it to occur when one of my friends (who is also my daughter's godparent) was in town after her birth. Neither godparent had time to take a class (they can take it at their local parish), but both are Catholic and are involved in their local churches, so I don't think it really mattered. So the bottom line is the only document we had to provide was proof that we, the parents, had taken the education class.
However, I'd add that you need to think about how you want your child raised. A baptism is a promise to raise a child in a particular faith. Do you want your child raised as a Catholic? If you want your child raised as a Christian, not necessarily a Catholic, you should find a non-denominational church that does infant baptisms. I think some of the other Christian churches baptize when the children are older.
The Saturday Long-Beach Press Telegram prints a listing of all the local churches by denomination with their phone numbers and a listing of the times of their services. That might be a good starting point for you.