The last time I needed to kill a racoon, I used a Remington 870 12-gauge loaded with #4 buckshot, because that was what I had nearby. In retrospect, a .410 would have been just fine.
I killed two with one shot each from a .44 special, but that was the very definition of overkill, esp. since I was about 5 feet away. In retrospect the .38 would have done just fine. (Finally, the perfect use for the 9mm round!)