here in se north dakota, i regularly shoot 20+ out of season (feb thru sept) coyotes. those areas will never be without an excess of coyotes. coyotes have three things that control their numbers; disease, food availability and other coyotes. if i shoot one, i'm letting another one live. as long as their established, you won't get rid of them without poisoning. you can't shoot them all at once and if you hunt too much in that area, they wise up. and if you can get rid of them, others move in in a few weeks.
every spring, each coyote pair has 6-10 pups. some die in the first few weeks, a couple more in the first few months, leaving 2-6 pups to find their own territory by december if they're males and next spring if they're females. do the math. they're not going anywhere.
so find the denning areas, try to get within 500-600 yards and play puppy distress and throw in some howling to get them upset. if they don't respond, move in a few hundred yards and repeat. keep a good open lane down wind as when they come, they come hard. and this time of year they're hard to see way out there. also, they like to sit out 500-800 yards and complain. those are my favorites. shot one at 585 and another at 653 the last two weeks. don't forget the bug suit and therma-cell.
i totally respect the people that don't want to hunt them "out of season" but i haven't sold a coyote for 2 years as they haven't been worth much.
plus, this time of year few are out there so you've got the countryside to yourself with low hunting pressure. so get out there and have some fun.