If you want to eat it and don't want to rely on headshots I can't help but feel like 22lr or 22wmr is the obvious answer?
THIS!
While 22rf and 22mag would be the best solutions for small edible game, they are not the best choice for coyotes. Yes they can kill a coyote but the reliability won't be there. Coyotes deserve something more powerful.
I have a 17 Fireball and a 221 Fireball and both those would be excellent for coyotes out to 100-150yds. Beyond that there are loads of choices.