A 20 with slugs might work, but it's nowhere near the ideal varmint gun. Save up your dimes & nickels, pull extra lawnmower duty, shovel snow--whatever you can do for money. A .223 would be perfect for yotes, but think about a .243--then you'll also have a deer rifle.

the 22. will work as will the 20gauge with a slug or #3 buck shot . its best to limit your shots with the buck shot to 35- 40 yds depending on how your gun patterns the pellet's ,you may get a bit more or less distance depending on the gun . and the slug to what ever range you can keep your shots in a paper plate .

I know it is a little pricey but I would try and go with a .223 or a .243. Nice thing about the .243 is that you then have added a versatile rifle to your collection for both coyotes and deer. Happy hunting!

You seem to be limited to a rather poor selection of guns for this work. I would not consider any of them suitable for the purpose. I agree with bat4bab, if you can work something like that into your budget.

Your 20 gauge with #4 buckshot will work within 40 yards. This is a pretty good rig for calling coyotes and you should be able to get them that close with good calling technique. If you want to shoot longer ranges as do most good coyote hunters, you will need a center fire cartrige and the small calibers work the best. I shoot .223 and 25-06 for longer range coyotes and they are great as are all cartriges in between. I highly recommend the very fast cartriges because the reduce the amount of lead you need to hit a running coyote, making it easier to hit them by far. This is important because about 80% of the coyotes I have seen have been running and at ranges from 100-500 yards.

Among all firsts, one thing that wasn’t a first for me was using a familiar and friendly cartridge. My coyote hunting has always been done with one small, deadly accurate, efficient cartridge: the .223 Remington!!!