I sure would. I' m not sure about NY' s laws, but i think it' s legal to shoot them year round, right? I personally wouldn' t be too worried about the cat population declining, but hey, I' m not a cat person. Plus, if you shot one arrow at a Coyote, and had 3 to spare, you still got enough for a deer. (should only take one shot).

Good luck out there.
-BJ