Just thinking out loud here...
What if you hang a bunch of clays on a net of some sort and let the shooter shoot a single slug for, say, $5. Most of the clays will have nothing behind them, but some would have some sort of prize card/color/whatever hidden behind them. You can hit up local gun stores and other businesses for cheap prizes (e.g. $10 Gift Certificate), or buy cheap prizes from ticket sales.
If it doesn't have to be a clay, you could also do a prize shoot with helium balloons. This seems a lot more practical to me. Stick a piece of paper in each balloon, some of which are "duds" and others that have a prize written on them. Just weight the balloons down or tie them to stakes or something and distribute them throughout a field. Slugs or handgun/rifle only, $5.00-$10.00 per shot, and the shooter gets to keep any prizes from any balloons they pop.
A local charity does the balloon thing, minus the guns, and always draws a big crowd. They usually have one big prize (e.g. a car or motorcycle), and the rest of the prizes constitute small items like gift certificates and small items. Any gun/hunting related stuff would be a great idea (e.g. ammo, holsters, etc).