You want us to help with scope selection, but we don't even know how you are going to use it. What range do you expect to be shooting coyotes at. What you need on the wetside would be considerably different than down in the Palouse. I've hunted most of central WA from the Columbia north to the Columbia and down along the coast until they closed most of the timber company lands. I never felt under scoped with a 1.5-6x42 and it has been my goto for most of the west. I did build a 22-250 for hunting the big winter wheat fields/grass lands and put a 2.5-10x40 on it, never killed a coyote with anything but 2.5x and just left it home, too hard on pelts. I'm finding the Athlon 2-12x40 to be very handy and have one on my medium weight 20P bolt action that I built last year, still haven't had to use anything higher than 2x down here in NM.
My AR wears a Konus Pro 1.5-6x42($150) with an illuminated circle dot, inexpensive scope that has proven to work well for me, clear, holds zero and the clicks were spot on sighting it in, I'm a set and for get guy as most of my rifles I can hold on fur to 300 yards, and if I have to take one that far I wonder what I did wrong on the stand not to get him in closer.
A Burris FF-II will get you started for around $150 and will sell used for not much less when you want to upgrade.