Apparently paintball is considered violent. When I tried making a club some lady told me "We don't sanction paintball."
That's when you describe how paintball is a non-contact sport, extremely low injuries, etc. Football is a way more violent sport and every school is ok with that.
Good luck trying to get the club started. But one thing that you have to think about is money. The DOE barely has any money to pay their teachers. Cut backs are a b%^tch and your club would be the first to go. Just make sure that you keep that in mind.
I wouldn't expect any money from the school in the first place. You are basically getting the memberbase (students) and if you are really lucky, some facility usage.