I marry my boyfriend and he has child support to pay and he's not working and I have his last name will I be responsible for paying his child support?

No... his debt remains his, but it will affect you because his debt will grow.. and it will reduce what money you have together as a couple as long as he is in arrears and as long as he has the obligation. Which is at a minimum 18 years... if he is in arrears it can follow him for life.

While the debt is legally his, and not yours... it IS going to come out of his pay and anything that is held jointly unless you can definitively prove and continue to prove none of it was his money. Which will prove to be a mightmare to you over a long term basis..