The quickway...
Shoot a deer or other game animal( in season of course!)and use the gut pileor get some big scrap pieces from your butcher and gut pieces and place them in the coyote's vicinity. Use new rubber gloves when you handle the meat so as not to scent up the area with your human scent.
Give the coyotes a day to key in on the pile. Set up a blind 40-50 yds away and use your 12 ga with #4 buck or T shot, etc with a full, or imp. modified choke. As such said coyotes are dining greedily at the pile, you should be able to dust 2 of them if your quick and good with a pumpgun!
Remove dead coyotes and wait for more on day 2!