Third recommendation for the Ruger 10/22 here. I've taken no less than eight (and and maybe a few more) Raccoons this year with my Ruger 10/22. I 've owned it since about 1980 and it has accounted for a lot of small game. It likes it's ammunition hot, and really works well with CCI Mini-Mags. Lately, I've been using a vintage box of Winchester Super X HP's to dispatch the vermin. Mine is topped with a 3x-9x-32mm Scope and is sighted in at 1 inch high at 25 yards. Most of my shots have been head shots and most have been one shot kills. I did have one very large Raccoon that took three shots to dispatch, but that was an exception to the rule.
I've also killed Raccoons with my old Bolt Action Marlin 782 in .22 Magnum, but that was at longer Range. Many years ago, I had to dispatch a Raccoon with my old WWII Walther P-38 and a 9mm Winchester Silvertip, as he had attacked my Cat, and refused to give up the Cat. Big mistake on his part. Had the Head tested and fortunately he did not have Rabies. The Cat recovered after being stitched up.
The only good Raccoon, is a DEAD Raccoon!