>>2490000You could maybe dent a local pig population this way using corral style bait traps to kill whole family units at once, but historical studies have shown that coyotes self-regulate their populations based on the number of individuals in the environment at any one time. A female in a territory with few coyotes will have a large litter and you'll be back to where you were within a generation or two.
Hunting coyotes is something that people do for fun or for practicing for actual game and just tell themselves it's good wildlife management or predator mitigation. Even when the US Govt had its mass poisoning campaign in the 1800-1900s coyote populations never went away anywhere for long, and I'd hazard a guess that thats been the most effective way of killing them in terms of raw numbers that anyone's tried.