I have shot a lot of coyotes and hitting them on the run is always the problem, along with trying to estimate distance when you dont have time to range them. we always second guess ourselves and try to hold high and lead these dogs. and 95% of the time its a miss. Here is the trick.. DO NOT hold off the hair. you will be surprised how much your hit ratio goes up on these running and "perceived" long distance shots. When I stopped trying to blindly compensate and just held on the hair I couldnt believe how many more I hit.. sure some were in the guts or butt, but it slows them down enough you can get a kill shot in them. The old time coyote hunters will tell you the same thing.
We drop close to 100 dogs a year, a good majority on video and somewhere between 10-20 are runners. Not holding off the hair completely depends on cartridge, caliber, distance, dog and bullet speed and angle. I'd have to say that in the last season, EVERY runner I hit (maybe only 3) was lead well off the fur.
My partner is noticeably better at runners, but he shoots daily and studies lead shots based on average running speeds.
The easy answer...it's just like shooting game birds. PRACTICE PRACTICE PRACTICE.
The more detailed answer is to just do the math and run the ballistics for movers.
Coyotes can crack 40 mph, but a nice average in "get the heck out of here" mode is between 30-35 mph depending on weather, conditions, terrain, age, etc etc etc.
My .243WSSM sending 105VLDs at 3000fps will have to lead in the neighborhood of 60-65 inches to score a hit at only 100 yds if the dog is moving full value. Hold on hair and you'll miss behind him.
The nice thing is that distance doesn't play as much of a factor because the bullet is covering it so fast. Between 100-200, the lead doesnt change by more than 3-4"...but change the angle too, and the coyotes speed essentially drops (because it's not full value) and then the hold greatly reduced.
My general rules to follow are...(100yds or beyond, additional foot at 500 yds)
2-3' feet out front (1/2 coyote length lead for full value runners.)
1-2' feet out front (hold on nose for a brisk trot or quartering runners)
Leading shoulder hair for quartering trots.