pay attenion to local laws
You could get in trouble dispatching them even with an air rifle. Like the others mentioned they can be treated as a firearm depending on the velocity.
Even trapping and killing them could get you in trouble with the PETA folks. Cruelity to animals charges don't look good on a resume.
In my state of NY you can't discharge a firearm/bow/crossbow/ airgun within 500 feet of an occupied dwelling/school/church, even when hunting ( except duck hunting )
You could also get fined for hunting out of season or without a license.
If I were in the same position I would find a lethal quick and quiet trap and don't tell a soul that you are using it. Its still illegal in most localities as you would be trapping without a license....so be careful.