EDIT: Sorry for the wall of text. :/
Actually dude, sex is already and act that both parties have to agree on before they begin unless one or both members of the union are mentally inebriated or disturbed in some way. Unless the two people are complete idiots with little to no education or concern for the future consequences.
Also, I doubt a contract is really going to mean anything when it comes to validating whether or not both members of the couple in question want to have sex or not. Also, sex just doesn't randomly happen, and someone always has to initiate the act, and if the other seriously doesn't want it, he or she would try to get out of it. And if the other continues, it's considered rape and the offender can be sent to jail or heavily fined depending on the offense.
Your idea of including a contract would just make unnecessary paperwork for people and probably put them off to the idea or they would totally ignore it altogether. You can't make people sign a contract just because you think it would benefit a few people who are having problems with girls or vice versa. There are already laws set up to protect people from unwanted sex and the consequences that would follow. In terms of having a kid, it's kind of the same thing as sex, both people have to agree to it and it has to be planned out. A baby just can't magically appear one day unless the mother had unprotected sex with another man and didn't tell her current partner. Also, there is such thing as Child Support. It doesn't matter if you wanted that baby or not, as long as that child is alive it is technically the parents' responsibility to make sure that child is provided the basic of needs for it to survive. Unless of course it is aborted or put up for adoption. Oh, and abortion was not, is not, and never will be free. Those surgeons have to get paid somehow, and it isn't on federal funding.
You seem to be really one-sided in this matter because the woman can be as equally to blame for having a child as the guy is. The guy is usually blamed more often though because of stereotyping, and if it really came down to it, the person that presents a better defense of the problem will usually win, stereotype or not. And women often are not seen in a positive light when they get an abortion. Especially not from their families. I know I don't view them in a good light because in my opinion, abortion is just an excuse to cover up a mistake and continue to sleep around without the threat of having to raise a child.
Besides, most of the people this would apply to are either still in school or drop-outs. If you have a good sense of when you want to start a family and your partner is okay with it, you shouldn't have to be required to sign a contract every time you want to have sex or have a baby. It's pointless, stupid, and only causes more of a hassle than preventing it. If you feel that by law women should not be allowed to have babies unless the MAN okays it, then you should just go the full yard and make unauthorized sex illegal too.
The only other option I see here would be to educate the youth. It's not 100% accurate, but it's way better than doing nothing only to be upset and whine about how it wasn't prevented.