I’m not sue that people from the different game an fish departments across the US are the same page in regards to controlling populations. Latest word that I heard “ if you over hunt the coyotes, they will produce more” (how many people did not know this) versus if you remove them there will be less of them to breed and we can eliminate them from an area. Coyotes will produce what the caring capacity of the area will handle; Rabbits run on a seven year cycle, you have more rabbits in an area, you have more yotes, less food less yotes. When you have yotes around populations you have introduced a new food source, the household pet, which will be replaced when one is removed. There is no way to remove all yotes from an area (yotes in NYC). Coyotes learn very quickly.
Here in Nevada G&F believe that coyotes and Lions are the main cause of the deer population decline, so they have hired companies to eliminate them (budget aprox $500,000 this year), they need to look at habitat or loss of the habitat and migration areas