If you raffle off a firearm, you will have to have a way to "credential" the winner (you can't put a gun in the hands of a felon)... could be problematic...
You have heard of walk-a-thons to raise money... you know, where each walker gets people (friends, family, acquaintances, etc.) to pledge an amount of money for every mile they walk... something like $1 per mile... they then walk 20 miles and collect $20 from those that pledged $1 per mile... the $ add up...
In this case they are going to stage a shoot-a-thon or maybe trap-a-thon or skeet-a-thon... Get donors to pledge $0.25 to $1 per clay bird broken (for the day)... Get an ammo manufacturer (or maybe the location) to sponsor the evert by providing the ammo. The team can take over a 5 position trap location for the day and shoot for bird counts... They can also offer coach someone (for a standard donation of whatever seems reasonable ($10 to $20)) wanting to improve their skills for a round of 5 position. Or maybe mini shooting clinics the day of the trap-a-thon. At a non-profit organization, they should be able to get some free publicity leading up to the event. You can publish it here. Maybe you can get a local TV station to do an infotainment news piece about the event if the team is really good - local shooters going to the nationals... If the publicity gets the public to come out for a day of shooting fun, the location will love them and be interested in doing similar events on a regular basis... could turn into a nice, steady cash stream...
Or if the idea works well, they could take the show on tour... run events at different ranges around the state...