The pellet gun might work if you're accurate enough. If not wanting to hurt them, I'd try a .22 at pretty close range, 20ft. or less, loaded with birdshot. If you can get them to vacate you'll need to take measures to prevent them from moving back in. Welded wire fence or something blocking access to under the deck. Raccoons are territorial and they will come back if they can.
We had a coon population explosion some years ago. I relocated a few. The last one I sprayed a dot of florescent pink paint on his back and took him to another drainage 5 miles away. He was back in 2 days. I began nightly hunts. 31 raccoons in as many days. A game ranger has told me that coons only have a 50 50 chance of survival when relocated as they have to fight their way in to the new territory.
If I were you I'd get a .22 for the same price as that pellet gun and practice with it a bit. You want head shots preferably as they have a bear-like layer of fat that makes body shots less than effective. One head shot will take them out where it might take 3 or 4 body hits and be less humane.
They are one of the chief vectors of rabies in this country and are bad tempered, destructive beasts.

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