The only thing you really could do is prove to them that you know pretty much everything about belly piercing, like the risks and how to really take care of it well. It's a bigger deal than a cartilage piercing.
And I guess you could ask them to explain to you exactly why they disagree with the belly and were fine with the cartilage because it's probably just because they think of a tramp when they picture one. And if that's why, then it's not really a reason! It's a double standard =)
If that doesn't work try to see if they'll agree to let you get it done for your 15th or 16th birthday. It'll seem far enough off that they might say yes haha
I think it's silly that so many people associate belly piercings with negative things. A piece of jewelry doesn't make the person, it's just jewelry. Sorry your parents aren't all that open minded! I got mine done at 14 too, and years later I don't regret it, I'm not a skank, and I'm in college lol. Good luck! <3
You could read this too if you want. It's about proper care and risks:
http://www.navelrings.biz/body-piercing-care.html
OH and you could also tell them that if they end up not liking it, then you can take it out after it heals and it only leaves a tiny little hole, not a scar like that other kid said.