If it was me, I would put a game cam on it for a while to confirm it is a coyote den, and get some cool photos. It doesn't actually look big enough to be a coyote den, or busy enough.
How did you find this place? It's not easy to detect if it's a coyote den without slightly obvious activities or seeing a coyote that got out from it. Good luck to your hunting plan!
One or two each long howl male, long howl female, wait 10 minutes. If nothing shows try pup distress off and on for 10 minutes. If still nothing try a coyote/fox fight or something similar for a couple minutes. Wait another 5 after ending the sound and see what happens. I'd expect them to show during pup distress if they show.
With the snow it should be pretty easy to identify if it's a coyote den by tracks.
There are tracks of varying ages all around the vicinity and heading to and away from the hole. Some very fresh some days old. Hole doesnt look big in the pic but im sure a yote could get in quite easily. Dont know what else it could be that the coyotes would keep going to and from day after day. Anyway the earliest i might hunt it is thursday. Went to park at the nf gate and hike up to call on saturday but a couple rigs of shed hunters were there so i figured id wait. If im unsuccessful at calling one in i will hang a tcam to watch it just for fun