I agree with what everyone else is suggesting. Offer to pay him his half of the money. I can see where your BF wouldn't want to just give him up if he paid for part of him. I also think that if the two of you can remain on speaking terms, the two of you could work out a deal. Maybe he can watch him every other weekend or something? If you need to go out of town, he could babysit?
Good luck! Breaking up is hard and even harder when you have a "child".