How can I get my sons father to give up his rights and still pay child support?

You can't.

He has an obligation to pay and a right to his child. You can't take away his rights as a father either way even if you didn't want child support.

If you browse through some of the hundreds of similar threads, you would have had your answer.

Generally its very hard to get a TPR. They are usually granted only to clear the way for an adoption or if the parent is a danger to the child.

State laws vary. Some states terminate both rights and responsibilities, others only rights. So you need to check what the laws are for your state.

So basically you want the best of both worlds? What does the father get out of the deal?