Instead of burying wire I suggest you look at an apron. You lay a piece of wire maybe 18” to 24” flat on the ground and attach that to the bottom of the coop or run. The idea is that a digging predator goes up to the fence, starts to dig, hits the wire, and does not know to back up. They are pretty effective. It’s a good idea to bury that about 2” to keep it out of the way of lawn mowers and weed eaters.
To attach it to wire you can use J-Clips, hog rings, or wire. To attach it to wood, bend that wire 90 degrees to fit against the wood then use a piece of ¾” thick wood to screw over the wire. Sandwich it in between the ¾” wood and the base of the coop with screws going through holes in the wire. Drill pilot holes for the screws so you don’t split the wood and make it easier to start the screws.
Don’t think coyotes aren’t a problem further south either. I just used Chicago as an example.