The 22-50 has it pretty well beat in ballisitics but frankly either round would work fine.
If you already have a gun that can handle coyotes you could just use that(a .22 would do just fine). If you had to buy a new one(or wanted to) then I would probably pick up the 22-50 for the better ballisitics.
I'm not a big time coyote hunter but fixin' to be. Right now I've got a 243 set up but think it's a bad choice if you want to save pelts. It was a present a few years ago from the Swamp Monster and I had to do something with it!
Now I think the 223 will beat the 22-250 because it should be more pelt friendly. Everywhere I look people are asking what bullet to use in the 22-250 to stop pelt damage. Well shoot a fragile bullet into something at high velocity and the outcome seem's pretty clear to me. Now the 223 has plenty to shoot a coyote out a good ways and has to be more friendly at closer ranges. Talked to a guy yesterday that does this stuff a lot and he say's, 223 with a 55gr Nosler flat base bullet, it's harder lead than the B.T.
There are times when the deer are simply not moving and you're forced to make something happen. Maybe you're up against a full moon or hot weather. This is when a silent drive to force deer to move should be considered.
By silent drive, you're not yelling and making a commotion to scare the deer. When deer are panicked, they're liable to bust out of the cover on a dead run, and any shot you get will be tough to make.
A silent drive is different. It means playing the wind to carry the driver's...