I really like to ponder the possibilities of where revolver tech would have gone if magazines had never been invented. So I would probably approach a new cartridge from that perspective.
This being the case I would like to see something like a .25 magnum. Maybe even go with a .27 caliber bullet to help distinguish it from other exisitng pocket pistols. A long but thin centerfire cartridge that you could get a 9-12 shot capacity with, 12-18" penetration from a 2-4" barrel, while still being able to use a breaktop revolver frame if you want. Would probably go with a Winchester silver tip style break apart bullet over a hollow point if a bullet other than a fmj was to be offered in the caliber.
However if I was really let loose on a new cartridge it would probably be to design a whole family from the ground up with as many different platforms in mind with backwards compatibility. Sort of similar to the organic growth of the .32, .38, and .44 family's, just planned out from the get go.
While we are at it an unrimmed shotgun cartridge might be interesting, but that would be a whole different thought experiment from a new concealed carry caliber.