It's s in his nature, that's his job. Just like you feeding your family.
When coyotes reach a certain population level there are checks and balances in nature such as sarcoptic mange to control overabundance.
They get a bad rap but they are incredibly adaptive creatures. While humans were successfully eradicating just about everything else at the turn of the century coyote ranges expanded despite the use of explosives, poison, trapping, etc.
Doubt anything you can do is gonna have much impact on a coyote population. Killing one wildlife species just to protect another wildlife species is is an irresponsible use of of a resource.
Haying equipment kills a lot of fawns too but.....
Trap