I recently was granted sole custody with no visitation for the father. The father is not on the birth certicate is there a way to terminate his parental rights

You cannot terminate rights when those rights has never been established.

First signing or not signing the birth certificate has nothing to do with ability to "sign over rights"

First since he has not signed the birth certificate he does not have any rights yet. ( unless he as has asked and gotten a DNA test)

But even at this point, he can't just sign over his rights, it does not work like that, if you have a new partner who wants to adopt, then you can get him ( after you prove he is the father) to sign over his rights to allow the adoption.

All that it is at this point, he only has the right to ask for DNA test to prove he is the father, so he can have rights