Decades ago, I read articles about cows and traps. They’re hard to avoid. But a couple guys suggested a big balloon or a white plastic bag tied to a fenceline. Curious cows are drawn to the movement (in the wind) and away from sets. Sounded interesting but I never used the idea.

Dale Billingsley’s sets hold more promise. Just don’t use salt type antifreeze

A four-coil #2 can hold them, I assure you.

Best advice is to get out of the pasture . . . but
If you gotta be in the pasture, dig a post hole. About half way down, make a shelf big enough for your trap. Put a good fresh meat bait in the hole and scatter some scraps around the hole. Cows avoid the hole but the coyote will eventually hop down onto the shelf and into the trap. Lots of a catches by both front feet. Hard boiled eggs make a good bait for this one; so does little chunks of lightly tainted venison. Good luck.

The bigger trouble i see with sheep even compared to cows is if one does step in trap your probably going to hold it were a cow will likely pull out. If it ain't your sheep that's going to cause some problems