Lots of good comments above, I'll just add to it:
My long time favorite was a 2-7x33 Vari-X II. Heavy duplex with crosshairs about the size of fence posts.
I hunted for years and never could figure out why anyone needed anything more powerful than 9x. A p-dog trip or two made me skew the upper limit up to maybe 12 or 14. That, and aging eyes when target shooting. Those 4-12's or 4-14's are looking better all the time.
Purely coyotes in your environment - pick something with as low a starting power as you can find. 2-7, 3-9, 1.5-?, etc...
Think you might do more of the varmint routine some time down the road then pick something out that starts at 4 and tops out at 12 or 14.