A lot tougher then people think.
I've shot quite a few coyotes with a broad range of calibers from .222 rem through 338 EDGE w/300g SMK's.
If you dont hit a coyote good enough to kill him on the 1st shot, he will usually run aways. He may or may not die.
Like another poster said, a coyote is not very big once you get all there haif off them, usually only 4-5 inches from stomach to back, thats not a very big target at all, especially when there moving. Anybody can shoot sitting groundhogs at 300 yards all day, but when things start moving, it gets a bit trickier.
Since were on the subject of toughness or bad shooting lol, the last coyote I shot was a prime example of there will to live, especially with bad shot placement. My dad hit him first on the run about 100 yards, hit him far back with a 117g SGK, he was spinning and trying to get up so I stuck a 50g vmax in him from my 22-250, didn't know where I hit him, but I could hear the thud and he was still spinning and kicking, flipping, he ended up regaining himself and took off running, I proceeded to lead him a bit and touched off another 50g vmax which was once again confirmed as a hit by the sound of the bullet and him hitting the dirt. I thought he was dead so I foolishly left my rifle at the truck and when I got about 5 yards from him you could clearly tell he still had a lot of life left in him. That poor coyote was all shot up, one of the back legs was about gone from the 1st 117g sgk, had a hole in his neck from one of the 50g vmax's. When I started to walk away from him to go get my rifle he got up and ran off once again. By the time I got my rifle and back up there, he obviously had enough gas to make it out of the country because I never caught up with him again. Do I think he lived, no. But that is just one example of a couple that I've come across over the years.