I am pregnant and the paternity can't be determined until after the child is born. I don't want anything from the determined father except child support, and neither of the two possible men seem to want anything to do with the child either. Can I receive child support from the determined father without having to give him custodial rights

Not likely. But if neither of them want anything to do with the child they/either of them can ask to have no custodial rights. But if he (the proven father) does want some visitation he will likely get it. Unless of course you can prove him unfit.

I am pregnant and the paternity can't be determined until after the child is born. I don't want anything from the determined father except child support, and neither of the two possible men seem to want anything to do with the child either. can i recieve child support from the determined father without having to give him custodial rights
It is not your choice to give or not to give him custodial rights.If you want to collect money-you have to allow him to be a part of your child's life.It is another story if he does not want to do eith the child.