Put a backing behind the set; like a log or clump of grass. This will force the coyote to approach from the front. Place the trap about 11 inches in front of the trap and offset 2 or 3 inches left or right. This is the approximate distance from the paw to nose when a coyote stretches to sniff the hole. When bedding the trap make sure the trap is bedded solid. Any play in the trap will cause digging. Use guide sticks as well, so the paw steps squarely on the pan.
One reason the coyotes could be digging the traps up is you may be leaving lure or bait on top of the trap. They will dig them up every time if you do that.
You could also have a digger fox working the sets. They have a tendency to dig up traps as a matter of pleasure.
The way to stop that is to bed another trap or two off to the side where the animal will step while circling the set.