My guess is that in all likelyhood you will wound the critter with an air gun if you don't hit him just right. If you can get him standing up looking at you then try to hit him right between the 2 front paws for a heart shot. Second choice would be a head shot, in the eye, or ear.
I doubt very seriously that you'll get a bang, flop and the animal will probably make it back into his hole. I'd suggest you use a shotgun, or "gasp" (I don't believe I'm saying this) call animal control and see what they tell you. However, once you get animal control involved it's hard to get them to leave you alone.
Are you bound by a firearm discharge law and thus prevented from discharging a fire arm in the city limits?