I would almost guarantee its not coyote for the digging isn't deep at all. A coyote would dig like a dog or fox. I would lean more towards skunk or armadillo. I am going by the size/depth of the dig and pattern of the dig/scratch marks its a body of narrow size.
I would guess they are after grubs or worms. I have never trapped armadillos, but have seen many having grown up in Texas. We have alot of skunk damage here in Il from skunks and they both seem to have common appearances. Are they all over your yard or just in one area? Do you use lawn fertilizers for moles and grubs?
My .02 cents.