Almost across the state Jersey municipalities have no discharge laws preventing from shooting on your property so this is more about discharging a firearm than drones. Now if you had some type of EMP device that wasn't covered under firearm laws...
shotgun is a bit overkill for sub/urban environments, although i agree it would be especially effective. i've never shot clay before and i was able to hit multiple times on my first clay outing.
however i imagine it would be no more than a weekend job to design a net-firing sabot or perhaps some kind of plastic scatter shot that could launch out of a t-shirt cannon.
My understanding (from an undergraduate US law class) is that you actually own the column defined by your property lines up into the heavens (and down into the Earth). You implicitly grant an easement (a formalized privilege allowing someone else do something with your property) to aircraft and other things like that. I imagine that this easement doesn't extend to drones doing something they're not supposed to.
Right now you can't : http://www.slate.com/blogs/future_tense/2014/10/03/new_jerse...