A number of things might work, but you need to be sure of what is legal in your area. If they are using trails, body grip traps or snares may help, but don't risk getting the nieghbors' cats if they are about. If you know where the entrances to the dens are, that is a better place to set up. I'm sure there is some bait that would work in a live trap--try a search on some of the trapping forums or do a search on Animal Damage Control. Obviously a rifle and a good rest would be the most efficient...or have the dnr import a couple of badger...lol.

An electric fence may do the job. Set a couple of strands short enough to do the trick and make sure you have a very good ground. There are solar units if needed. If it is an area where people walk, make sure there is a sign up to avoid litigation. The fence won't "fry" them, but a good jolt or two would likely discourage them from heading in that direction.