Sounds like it could be a coyote or fox, they are more likely to dig to access a coop where a coon likes to find a forgotten hole or gap to sneak thru, but it could be a coon. Look for footprints in the dig area (fox are small oval impressions, coyote is a dog type print, and coons prints look like small human hand prints) A #2 coil spring or jump trap works nicely in your situation, they are compact and easy to set. Pull the loose dirt out of the hole, set the trap in level & flush with the ground, lay a piece of paper or a few large leaves over the trap and sprinkle the dirt lightly over it for camoflage. The paper / leaves will prevent the dirt from interfering with the trap's operation. Sprinkle a smelly oil or juice on the dirt to encourage the varmit in and to cover the scent of the trap and you. Also suggest you closely inspect your fence for holes or gaps (they got in somehow) and you may want to set trap or snare there too. If you live in a urban area and hesitate to do your own traps, maybe your local animal control will set some traps for you and they handle disposal. Your are correct in taking action as this critter is not stopping until the birds are gone 'cause critters like easy meals like chicken! Good Luck
