One good option is a .32 or .38 rimfire. You can fool around with custom cartridges that shoot a 32/38 caliber ball: http://32rimfire.blogspot.com/
More work, but better results, IMO, can be had by making, or having made, inserts that hold .22 WRF (it's like a short .22 Mag, not very popular, but still produced) and line the barrel with a .22 barrel liner. If you're concerned about the value of the antique you're modifying, you can do this all reversibly -- just sand the barrel liner and inserts to fit, don't modify the gun, and install them with loctite. But really, you can find these rimfire chamberings in relatively worthless and plentiful guns anyway -- so-called Suicide Specials, Iver Johnsons, that sort of thing, in crappy cosmetic condition.
For centerfire options, you'll probably be stuck reloading, but there's tons of European stuff, like any of the more-or-less interchangeable .450 Adams, .476 Enfield, and .455 Webley cartridges. There's also plenty of pocket revolvers in 5.75 Velo-dog.
.320 Revolver, which is similar to .32 Short Colt (Colt actually copied the European cartridge), is an edge case, as the Colt cartridge has a bigger rim -- some guns will accept .32 Short Colt, some won't. Not sure if that's a problem for you anyhow.
And there's any number of European military revolvers in their respective cartridges, though you may find these rather large for concealed carry. Someone's already mentioned the Nagant, but French, Swiss, Germans, everybody was getting revolvers made back then.
The third option is getting an antique cap-and-ball revolver, and a modern conversion cylinder in a cartridge too new to be on the list, e.g. .45 ACP or .38 Special, taking care to only shoot loads equivalent to the gun's original blackpowder loading. The modern conversion cylinders are made to fit modern repros, not original antiques, but with some fitting I expect they can be made to work.