Is he sure the baby is his? If she is sleeping with all of his friends, is there any room for doubt?
It's great that he wants to "do the right thing", but has she actually asked for support from your son? If he has no steady job, he is only going to be able to help in a very limited way (at least at first) anyway. What were his plans before this? Is he in school/planning university, or is he looking for work?
I know it's his baby, and your grandchild, and would hate to be in this position myself - but would he be able to walk away, if the woman is not asking for support from him? I can't believe I suggested that, because I wouldn't be able to walk away from a grandchild of mine, but it's easier to be dispassionate when you're not directly involved, and it may be the best outcome for your son.
Does the woman definitely want the baby? Again, easy to be dispassionate, because I couldn't give up one of my babies, but if it really was a mistake, she might, for example, be up for you offering to adopt it or something.
Whatever - it's a horrible situation, for you and your son. I really feel for you.