I shoot at a friend's private property so we have free reign on what we can shoot. We shoot all sorts of targets, from paper, bottles, cans, old electronic devices, steel targets, etc.
Depending on what is allowed on the range that you use, here are some suggestions:
1. Do some sort of competition with both long guns and pistols. A good challenge for paper targets is like playing knockout. Basically each shooter gets one shot and whoever is the closest to the center wins. You can do this individually, in teams, guys vs girls, etc. You get the point.
Another idea with handguns is, you can try long distance shots with pistols i.e. 50yards or more. You can use paper plates instead of traditional targets too (its cheaper!). For example, set up paper plate targets at 50yards, let each shooter shoot 10rounds from a handgun, then count who has the most hits on the plate.
2. If allowed on your range, shooting bottles filled with water is fun. Set up a few bottles at different distances on a rack or on the ground. Have each person shoot the same number of rounds and whoever shoots the most bottles wins.
If possible use plastic bottles (water bottles, 2liter soda bottles, etc). We normally use glass bottles of different sizes at my friend's property, but be careful with broken glass.
3. Balloons and other exploding targets like eggs and fruits are another option if allowed on the range.
4. Clay shooting with shotguns are usually a lot of fun. You can use steady clay target holders, or clay thrower if available.
5. Steel targets are the norm for most ranges. The farther the better of course. Set up some competition rules like Iron sights only, different shooting positions (prone, kneeling, bench, etc).
As always, clean up after yourselves, have fun, and follow all safety rules. You may not be able to do some of the things I suggested, so use common sense and do what is allowed by the range.
Congrats to you guys!