Problem is that thinning out the herd doesn't work. It's been proven over and over and over. Every predator exists at carrying capacity, and every year more are born than could possibly be carried. As many young survive as oldsters die. So you kill more oldsters, more young ones survive. The herd numbers never go down; they always stay at carrying capacity as long as the species is numerous enough (which canids and raccoons certainly are).
It goes like this:
Carrying capacity of 1000 acres (of which your chicken coop is one corner) is, say, 20 coyotes. This is about two packs.
Each pack produces six pups a year. Now there are 32 coyotes in the 1000 acres. 12 coyotes must die.
If three old-lady coyotes die, three pups (on average) will survive. The population remains quite stable over many years this way.
If three old-lady coyotes die and you shoot seven coyotes, ten pups will survive. Come winter there will be just as many coyotes in the 1000 acres as there were a year ago.
Removing animals doesn't work. It might make you feel better but the vacuum will fill almost instantly, and it'll fill with young stupid predators who are willing to try anything.
DISCOURAGING animals works. You want to have the existing coyotes decide that your coop is not worth the calories. Once they decide this, they'll stay away and you'll buy yourself years without coyote predation, instead of a constantly cycling problem.