I am married and we are fixing to get a divorce we have one child together and one on the way, he wants to sign his rights over to the unborn child can he do that?

Did you read this (https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html)? Who would he sign over his rights to? Generally, it can't be done except for an adoption.

There is this myth that a parent can just sign over their rights. ONLY a court can terminate parental rights and courts will only do so under specific circumstances. They will NEVER do so to allow a parent out of paying support.

When using a site like this it's a good idea to browse around first. You can often find a FAQ (like the sticky AK linked to) or previous questions that will have answers that bear on your question.

The divorce won't be finished until the second child is born and the courts can rule on it. And no he can't just sign his rights away he will have to pay child support whether he likes it or not.