In NY it would be very illegal to shoot a coyote out of season - for any reason.

Personally, I don't think its wrong to thin the predators if done legally. But in my mind the coyotes have as much right to feed as you do. Maybe it would be easier to increase your rabbit population with brushpiles, or mow fields and leave the Hay on the ground to increase the mice population. The coyotes (and other wildlife) will benefit - and predation on deer should decline.

We will never elimiminate coyotes. They will take some deer - but if we manage the land so that they aren't forced to feed on deer - then you can reduce the problem.

States like NY offer Liberal hunting/trapping seasons for Coyotes and other predators - if you cannot work within the 7 or 8 month season to reduce their numbers, then your are just breaking the law in my view - and should be prosecuted.