Good questions. We run our club off of funds generated by participant fees. All of our 3D's and Target archery events have a fee. Yea want to play yea have to pay. Kids under 16 free for the 3D's I'm not sure on the Target stuff.
If any fee is charged for your whole event but not individual happenings within the event try to get a small cut of the whole pie so you can generate a little moneies for your archery events. Be straight forward if the archery events don't get some finacial help from the organization they are going to go away.
Sometimes you can get gear or targets or what not donated and make agreements to have sponsorship posted at the event or near the shooting line or near a target.
Some outdoor stores have given us some nice doorprize gear at HUGE discounts. We still pay some but no where near retail and many times below wholesale. Talk to a manager, make sure you will tell them your organization will send people their way.
See if people in your organization have employers who have matching donation programs within the company.
Write the letters to the archery manufactures. Include your community service work, include the number of kids your trying to get involved, include the number of participants. Let them know that they will get recongnition at the event, in newletters, on web postings.
Just some ideas Good Luck!!