Your question is a good one. Other than grass, and certain types of trees, the deer eat everything. I am about an hour outside of Ithaca and we have the same problem here, MASSIVE numbers of deer. Every day herds of them wander around my yard, crapping everywhere - and I am very close on to a major roadway and rather busy business area. The local nature nuts are very active and whenever the sensible locals try to have something done - we get drowned out.
So, now we all put big nets up. Have to put streamers on the fencing because the dear will jump straight through. Our yards look like hell, but if we want anything to grow we have to fence it or net it off.
I figure once enough of their kids get lyme disease they will get past the desire of protecting bambi. The tick problem has gotten bad bad BAD.
My problem out in the desert is rabbits. They like to eat anything I plant, so I have to erect small enclosures to keep them out. I'm a big fan of coyotes though. They are everyday visitors on my desert acreage, and occasionally I see one pass by with a rabbit in its mouth. Nice to see Nature at work...
What you need is a 25 cal air gun, with night vision optics. Rifle makes minimal sound, the round is subsonic, and you shoot them at night as no one will hear or see you. A head shot will kill it, but be prepared to dress the deer at night. Alternatively, a belly shot will give the deer a case of peritonitis, and it will likely run off and die elsewhere.