I am a teacher as well and even though we're not an official club at our school, i have a large group of students who are on a team. As their sponsor and a former player, I had a few ideas up my sleeve.
When I played at Eastern Illinois, we were fortunate to have a member own his own paintball business/field. We got awesome discounts on paint as well as field time when ever we wanted. The thing he wanted in return was the team to come out and help fix bunkers, pick up brush from a storm, etc. Some hard labor at your local field should hopefully get you some love.
The other thing is organize an all school trip (clear with the administration first and do all the necessary paperwork). Find out what your local field can handle and how much they will charge for the event. Add an extra $5 on to the tickets you sell and keep that for your club.
Run a tournament. At the same local field from my college days, our team acted as the refs and other workers (selling paint, filling air, etc). The owner/co-player let us take all of the entry fee and some of the money off of each case of paint. You still have to come up with prizes, but take some of the entrance money and offer cash payouts or a few cases of paint/field passes. If you have a large enough club and the field is large enough, you might be able to delegate other workers to run the fields that aren't being used by the tournament to make sure the field owner isn't taking a huge financial hit on a weekend.
Last but not least, high school players and teams are the best bill boards. When reaching out to pro shops, make sure you tell them how many kids are on your team or in the club, then tell them the size of the student population. For instance, I have 30 kids in our unofficial club and we have a student population of 1700+. The pro shop who sponsors us sent us company shirts to wear around school so now the entire student population sees the name of that company and are more inclined to buy from them.
Hopefully some of this helped.