That's a tough situation you have.
Out here on the open plains, coyotes come out as the sun goes down, and because there is only grassland, no trees or hills, we can hear them yipping
and howling from miles away.
The ranchers around here will shoot any coyotes they can and then skin them and hang the hide on their barbed-wire fences. I think the scent of dead
coyote scares the live ones away.
I have a small herd of mule deer that come in from New Mexico (about a mile away) and have taken up residence on our acreage. I am delighted by their
presence, although they are exceptionally fast and run away if they smell humans. My husband tells me that if the herd grows to 5 or more, the
ranchers will start shooting, because they don't want large herds of them competing for food and water with their cattle. I'm hoping that doesn't
happen, because they shadow me as I walk in the evening and they are such beautiful creatures.
In your case, there is no easy answer. If the deer are allowed to breed without any checks and balances, they will be everywhere, hungry and scrawny,
and then they cause accidents by wandering on the road. If the coyotes are allowed all the critters they can trap and eat, then you have a coyote
problem, where they also get hit on the road, and gobble up cats and small dogs.
If you want to stop the coyotes, get a coyote whistle from any sporting goods store, get out at sunset and call 'em. Then plug 'em, and leave the
carcasses as a warning to other coyotes. That will give you some peace, temporarily, but there is the larger issue of human encroachment on wildlife
habitats, and the natural balance of nature in the wild.
I know some people will think this is cold-hearted, and I do apologize to those of you who are uncomfortable with the killing of coyotes. I
personally do not kill them, I simply bring all my cats in at sunset and let the coyotes do their thing.