My children's father ask me if my husband wants to adopt our children if I say no can he still waive his rights and not pay child support?

No, He will be responsible for child support so long as he is the legal father of the child.

Your father can not just give up his rights, he can give them up if your new husband is willing to adopt. If he is saying he can just give them up, he is lying. He will have to keep paying unless your husband is willing to adopt.

There is this myth that a parent can just give up their rights. If you would have browsed around this site, before posting, you might have found the Family Law forum where there are sticky notes dealing with this issue as well has hundreds of threads dealing with this issue. I mention this to help you more quickly find answers in the future.

The bottom line is that only a court can terminate parental rights. And no court will terminate rights just to allow a parent out of playing support. That's why he wants your husband to adopt, an adoption will terminate his responsibilities.