I did it for several years as soon as Kentucky allowed it.
It is DIFFERENT than you are used to hinting at night and you need to get much closer. I don't know what's allowed in Tn but I used Hevi-Shot Dead Coyote 12 ga, 3 1/2 inch "T" shot.
You need good red lights as well as a shooting light. Go outside in the dark and have your wife hold a flashlight above her head pointing it at you then turn it on. No matter how hard you try you cannot see her, neither can the coyotes BUT they can and will smell you. You will see their "eyes" long before you can see them in any light.
Every coyote I killed at night with my shotgun was within 50 yards. Every one of them was coming to my caller I had set up crosswind. Think of it like this. I put the caller 30-40 yards north of me with the wind blowing toward the west, east of the setup is a known spot coyotes use. I would set up facing the northeast. Remember they are going toward the caller, not me. Some coyotes came from the north, out of range, some from the west, and picked me up. The one I was after would come in from the northeast moving south to circle around to get wind of the caller. I would pick him off when he came into range.
As soon as Kentucky allowed rifle hunting at night I quit using my shotgun.