Trouble is, you kill one, and another moves right into his now-up-for-grabs territory. Better to make the coyote afraid of humans and afraid of coming anywhere near your house. Once you have “trained” the coyote who has staked out your neighborhood as his territory, you’re better off with him than a newcomer who has no qualms about coming near people and houses.
The best method for training a coyote is high velocity lead.
Leg hold traps work well also.