My son wants to give up his parental rights for his daughter, Will he still be liable to pay child support?

Yes he would still have to pay unless she is married and the husband is willing to adopt or
She agrees that she is soooo financially stable that she does not want his money

BUT the court is not going to allow termination or discontinuing child support without her marrying and her husband stepping in to adopt.

I think it is extremely rare, if at all, for termination of rights if there is not a remarriage and an adoption.