Mostly we used a 22lr. We used a marlin, a ruger, a stevens or a remington. Any 22lr will do the job on a coon. He should be able to find a used 22 for less than $200.00. If he has a shotgun that will work too. Nothing smaller than a 20 ga though. The coons will just climb higher and a 410 will become ineffective. I sometimes carried a 20 ga H&R "topper jr". Sorry if that answer was too vague.
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For info purposes only, use it at your own risk. JFKimmons and G&G aren't liable for it's misuse.
You know if you had a dog like the one my grandpa used to have you wouldn't need a gun.
Tigger was a Blue Tick that we used to hunt with. The nice thing about Tigger was that all you needed to do was set your skinning board outside the door and old Tigger would go out all by himself and catch a coon that would fit that board. Great system! It worked great until grandma set the ironing board outside the back door one day. Poor Tigger's probably still looking for that coon...
__________________ But if you do wrong, be afraid, for he does not bear the sword for nothing.
If shooting at night a cheaper Marlin type sight is best the worst night time open sights were Rugers, mabe those red dot type optical sights or red dot laser would be a option if allowed in your area, A good gun that feeds and you can clear the chamber for safe carry is important, Rugers were good for that by droping out the mag and clearing the chamber, pump and lever rifles were good too.
We used allot of Rugers and put up with the fuzzy sight's, Marlin model 60's, Remington semiauto's, and a winchester 9422 because the feed system you could load anything in it and it would feed it and the semi buckhorn rear sight wasent all that bad, a old guy actually had a sight tube taped to his old mossberg it was basicly a 6" piece if 1/2" electrical conduit that was used as a very crude peep sight he never missed come to think of it, down right accurate when clearing "christmas trees"
"coon loaded cottenwood tree on edge of a corn field" all those glowing amber eyes lit it up just like a christmas tree.
if you are hunting them at night in rough terrain, I would look for a nice old mossberg, they are accurate, and fairly cheap. If trapping, a long barreled 22lr, pistol, easier to carry, and still accurate if you practice with it. No matter what you choose, you need to make sure you can hit what you are aiming at.
coon gun 
