They do make revolvers that will fire both, but the cylinder has to be swapped out in order to accomodate the caliber change. You cannot simply place a .22LR into a .22Mag and expect it to work safely and well.
NAA makes mini-revolvers that convert from one to the other, not sure who might currently make a full sized one that does. Somewhere around here I have an icky old HR that does it, too, but they're long out of business.
Edited to add: I've never seen a DA that does the trick. Not sure how that would work, mechanically, though I'm pretty sure if someone put their mind to it they'd figure out a way.
pax