I have quit a bit of experience with this. I was in your shoes when I was stationed at FT Carson, CO. I wanted to get into coyotes and bobcats. I had a 30-06 and a 12 guage Goldhunter. I used to 30gr acc for the 30-06 and blew two yotes to pieces. It didn't sit easy with me. It seemed a waste. So then I researched different rounds for the 12 guage. It came down to T shot, and Coyote heavy loads. The later cost to much so I went with a 3 inch T shot. I called a yote in and dropped him at 47 yds. I know some will say you need a reach out and touch'em gun. I shot 8 yotes and a bobcat last year. More then half were within 50yds. The only one was the bobcat I dropped at 250 yds with my .204.

Long story is you can hunt yotes with ur 12 guage. Just use the right shells.

My uncle hunts yotes in norhtern wi. He goes out at night with a night spotlight and hunts over guts piles after season. He's had some success with that.

Good luck