Question, why do you want to get it done? Make sure you want it for the right reasons first.
Next, assuming you feel it important enough to you and feel validated in those reasons ask why he'd want to break up with you over it and hear his reservations about it. If he can't change your mind ask him if there's a compromise you can come to, like helping pick your piercing or getting one that isn't as noticeable, otherwise it might not be avoidable.
(No idea why Pebyron blocked me. I would have just +1'd his answer and left this as a comment, but, whatever...)
I say Pebyron said it quite nicely. Don't change your body unnecessarily. and indeed your boyfriend is a moron if he broke up with you over something so stupid and petty. Your choice is which you want more, but really, your boyfriend sounds like a dumbass.
You do what you want with YOUR body. First of all, you're under 18. There's about a one in 100,000 chance you're going to stay together forever. Secondly, do you want to be dating a guy who would break up with you over a belly button ring? Or WORSE, who would blackmail you? Blackmail is so utterly disrespectful. There is no love in such a cowardly action.
But seriously consider if YOU want the belly button ring. They're cute at your age, yes, but they are PERMANENT.