A one-piece mount, vs. two separate rings, should really help. You have a lot more surface area contacting the dovetail to add more friction to keep things in place. Also, make sure your mount is mating up with the dovetail appropriately. Cheap mounts/rings may require you to file/fit them so that their angles match the angles of the dovetail.
Note that .22LR dovetails are typically spec'ed at 3/8" width. Whereas airgun dovetails are usually spec'ed at 11mm width. Which is your mount/rings? Is it the same as your dovetail? And to top that off, both .22LR and airgun dovetails vary from this spec, as do any mount/rings you may have. The cheaper they are, the more they tend to vary. Luckily, .22's don't recoil much, otherwise I'd expect them to be throwing their scopes across the range regularly, with all this slop in mounting. Airguns, at least the "springer" variety, recoil more, and in different directions, and those are the guns that really need scope stops. .22 rifles? Not so much. Check the fit and how well your rings match the dovetail you're trying to attach them to. Don't be shy about filing to correct a poor fit. A little jewelers file is what you want to use, not your giant lawnmower blade sharpening one. A one-piece mount, at the quality level you need for a .22, is cheap. e.g., this one for $14.95
http://www.pyramydair.com/s/a/Leapers_Accushot_1_Pc_Mount_w_1_Rings_3_8_Dovetail/805