Say a woman gives birth to a child and wants to give it up for adoption. The Father is totally against this and is willing to raise the child alone. Can he sue the Mother for child support like a single Mother can sue the Father?
I infer that you are asking about an illegitimate child. Different states have different laws, but GENERALLY speaking, a putative father must petition the court for custody of an illegitimate child (which are often given by statute to the mother’s custody). He’ll need to prove paternity. If the mother wants to give up the child for adoption, the father will undoubtedly get custody, and yes, he can petition the court for child support. A parent generally cannot voluntarily give up their parental rights JUST to avoid paying child support (otherwise too many people would instantly do that upon the birth of a child and parents are generally legally obligated to support their children). So the answer to your question is, yes a father could get custody of the child and could also get child support from the mother.
YMMV depending on your state. I am a lawyer, but I am not your lawyer; I do not represent you; I do not even know you and I am probably not even licensed in your state. This is not legal advice, just general information from an anonymous source on a public message board.
Adoption requires the consent of both parents, if both parents are known. There are many cases where the mother is known but the father is unknown, a few both parents are unknown (in the case of foundlings) but very very few where the father is known but the mother is unknown.
So you hear all the time about a mother putting a baby up for adoption without any input from the father. But in a case where a man stepped in and could prove he was the father, the adoption could not proceed without his consent.
Of course, the next step is determining custody of the child. Even though the mother might have been in favor of putting the child up for adoption that doesn’t automatically give the father custody. It would proceed just like any other custody case.
Not to worry, I don’t have an illegitimate child, I was just wondering. I live with the Mother of my daughter, she would not give her up for anything, and I don’t have to worry about child support. 
This was just a question out of curiousity.
Thanks for the answers though guys.