Coyotes are different than wolves in that the more we kill them, the more coyotes there are. If there were no coyote hunting, there would be far less coyotes.
That's not a true statement. Coyotes do have the ability to have larger litters when food supply is high and visa-versa, BUT if we stop hunting them there won't be less, UNLESS their food supply declines, which would have to include everything they eat, and what they eat is a very wide variety from insects, fruit, and anything of meat. About the only two events that I've ever seen have a great impact on coyote numbers is disease and severe drought.

I challenge you to find any cattle rancher that wants no coyote hunting on his land because he believes no hunting will lead to fewer coyotes. You would think if no hunting equaled fewer coyotes, a rancher would be the first to know it.