You really need to earn the money yourself. Paintball is expensive and it is hard to get parents to understand the sport part of it (yes it is a legitimate sport, but it isn't mainstream).
It is expensive! Your cost is $300/month, which for some is cheap, but for parents that is a lot when they probably didn't pay that much for your whole baseball season.
Depending on your age, you'll need to get a job. If you can't find a real job, then you're going to have to mow lawns. $300/month isn't too hard, that's $75 a week. You get 3 or 4 lawns once a week, and you're set. Also, work for the field. Offer to clean the staging area, mow their lawn, help set up the field, etc (notice, this isn't even reffing so keep that in mind).
Keep all conversations civil with your parents. Yelling and arguing is a great way to kill hope of them agreeing with you. I've been a manager of other people, and am a parent, and asking nicely and calmly always has a better chance of me saying yes than arguing does.