Coyotes reproducing more/faster when population densities drop is a very well documented phenomenon. For top predators to regulate/suppress coyote populations we're talking about large numbers of those wolves over large areas.
That's a much different situation with different dynamics than "lets shoot a bunch of coyotes", I think it should be very easily seen why. Niches and their exploitation, yknow? WTF good does it do to increase your population density when the problem is that more successful predators, in much larger numbers, are already dominating your ecosystem? All of those extra offspring will not survive to reach reproductive age.
On the other hand, in an area in which those top predators are NOT present in sufficient enough numbers to be a limiting factor, the population booms when density falls do actually serve a purpose.
Summary/bottom line: suppression by wolves is a function of how many wolves occupy how much space and monopolize how much of the resources of that niche, besides causing direct mortality.
BTW, for anyone who likes learning more about coyotes/our history with them and control, check out Dan Flores' "Coyote America: A natural and supernatural history"