Eastern Coyotes don't stay still for very long, at least not the ones that I've hunted/shot/missed

(I'm assuming eastern, due to your location)
For that reason alone, you'll need quick target acquisition, which includes some potential close range range shots, (50yds) depending on where you're hunting of course. I don't disagree with the suggestion of a 3-9, which was noted above... It would be perfect for what you're using it for. I've had many groundhogs pop up at 25 yards, and I couldn't get on them because I had my high-power scope cranked up at the time.
As far as having enough power to see bullets holes at 300 yards... Use a spotting scope in this case.
A bit of mirage, and I can't see my 6mm bullet holes at 300yds with my 32x Sightron or my 32x NightForce.
I guess my point is, if you go high power, you might as well go 32x + lol! (give you self a chance to see bullet holes when shooting paper)
If not, do the basic 3-9, or maybe a 4-12. They fit well into the typical north-eastern woods and field layout.
just my .02.... but, of course, the cat can be skinned in many ways....