Breen (1989) claimed to know of two Proof 1822 Dimes (at least one of which he had seen) and a third that had been reported to him. According to Breen, some purported "Proofs" were "first strikes or buffed pieces."
Davis et al (1984) wrote: "Perhaps three proofs exist. Finest seen is Proof 65 (Lot 467, Numismatic Gallery's 'World's Greatest Collection' Sale, Apr. 4, 1945.
PCGS has certified three Proof 1822 Dimes: two in PR66 (which may be the same coin) and one in PR63.
Sources and/or recommended reading:
"Walter Breen's Encyclopedia of United States and Colonial Proof Coins 1722-1989, New Revised and Corrected Edition" by Walter Breen (1989).
"Early United States Dimes 1796-1837" by David Davis, Russell J. Logan, Allen F. Lovejoy, John W. McCloskey and William L. Subjack (1984)