I am with a guy who is not the father of my child. The father doesn't want anything to do with the baby can the guy I'm with now sign the birth certificate as the baby's father?:confused:

Not legally, if he did, and the real father ever wanted rights, he would merely sue, and in fact this is fraud.

So after the baby is born, you get the father to sign over his rights to your new partner to allow them to adopt, this is the proper way to do this

As fr chuck said your new partner would have to adopt your child! Good luck with it all.

I know people that do that and then the problem is they end up breaking up months or years later and the non biological father is responsible for years of child support which is not fair to him. So do it the way Fr_Chuck said, have the real father sign and then marry the other guy and have the real dad sign over rights.