We don't know if he is calling coyotes or just shooting targets of opportunity. Actually many can shoot pretty fine groups off shooting sticks to make higher magnification useable just watch some of the winners at the PM Egg Shoot. Reticles have a big impact also. I've shot a 6x scope in a Egg Shoot, but the reticle was very fine(almost useless as a hunting scope), you could hold very close with it and I've shot higher power scopes that the reticle so fat you had to place the egg in a quadrant as the reticle was so fat it made the egg disapear(great for target acquisition in low light or heavy cover)
If I had a choice between a 2-12 or 3-9 I'd take the 2-12 with its 1/3 larger FOV on the bottom end (faster target acquisition, easier to track a moving coyote in the brush) and a 1/3 more X's on the top end for finer long range holds and load development.
The terrain you hunt, your shooting ability, your calling ability and how you hunt will all play into the ideal scope selection.
Even in open country my scope never comes off the lowest power until needed, if the coyote is far enough away to need higher power there is time to turn it up. If the coyote is charging in or appears at your bootlaces there is no time to turn the power down and reaching up to do so an spook a close in coyote.
Paralax adjustable scopes, leave the parallax adjusted at 200 yard, if they are farther out than that, there is time to adjust, closer in the parallax adjustment won't make a big enough difference to cause a miss on a coyote, nor will having a slightly fuzzy coyote at 20 yards.