Try "rimfire" instead of .22 LR.
AFAIK, no one has converted one yet but it shouldn't be too difficult. Take a .22 bolt from another firearm and make the necessary mods to make it slide back and forth in the AK. The Remington 590 style system where it rides on two rods would seem ideal. .22 bbl liner down the bore of a .30, chamber adapter for a .223.