You cannot remove coyotes from your environment. It has never worked and never will. Two things will control coyote populations....spay/neuter or actually vasectomy/tubal ligations, and wolves.
Since you are not in a position to employ either of those, your best bet is to deselect only those annimals that are aggressive about approaching your home and your animals from the gene pool. Leave those that are not that way alone. This slants the dna passing competition to favor less aggressive animals.
Deer do not need protection from predators. Deer need protection from humans that kill off the predators that control their numbers and thus prevent mass starvation and disease resulting from deer overpopulation.