Hmmm, if you try to use your 3 year old child to bribe him to stay, it will only make him want to leave faster. You need to sit down with him and have a proper conversation and see if you can salvage anything from what is obviously a failed relationship. But , really, you should have brought it up long before it got to this stage as once its passed a certain point, there is usually no return as the decision is already implanted in his head. I bet he would have met someone else by now also...
Just ensure that you have appropriate visitation days and dates in place. I'm sorry if that sounds clinical but you can't force him to stick around. Hence making sure that you have prearranged days for him to visit. It's damage limitation.
is his name on the child's birth certificate as the father? If not, make sure he gets it on there before he moves away, it will be easier to get him to cough up support when his child starts school or needs to go to college or have driving lessons. Oh and ask him before he vanishes if he wants the school to send a seperate set of school reports for him and medical questionaires, oh and double check his blood type so that if the child (god forbid) is ever ill there is another close relative handy, and ask him if he wants to see photos of the nativities or will a quick email update do.
You can't convince him and even if he did chances are he'd be miserable and resent it and wouldn't it be better for your child to have a happy father he sees a little less often than a miserable one he sees all the time?
If your ex is unhappy and wants to move then chances are he'll do it anyway at some point anyway, when do you think he should stay until? His 16th, 18th? Maybe it'd be better for the child while they are so young rather than when they are older and may be affected more by him leaving?
Is it just because of the child you want him to stay or is there a part of you that is wanting him to stay for you.
I really don't mean to be blunt and hope it all works out for the three of you xxx