The coyote is probably the most successful predatory animal in North America. Contests like this have little effect on the coyote population, which over the last hundred years spread from the western United States to all of North America because of the elimination of the wolf and human induced ecological changes that increase coyote habitat. The capacity of coyotes to increase their numbers in face of substantial killing also promotes natural selection in favor of a more adaptable and durable coyote population.
The question about contests like this is ethics, and I think the controversy is basically a conflict between rural values in an area of human population decline and those of the larger society.
Coyote killing contest prompt howls from foes. Town offers cash prizes in calling competition. By Matthew Brown. Billings Gazette. AP
New, posted on 1/12, article by Todd Wilkinson. Controversial Contest Brings Coyotes Again Under The Gun. New West.