Due to the popularity of Cowboy Shooting, .38 Long Colt (which was Army issue from 1892 until 1909) is commercially available, and not too pricey, considering.
http://www.midwayusa.com/find?dimensionids=10068
Your gun may chamber .38 Special (some Long Colt guns can), but firing such is a risky proposition.
I recall the cartridges that were kept with the revolver were wadcutter rounds that were seated nearly flush with the case mouth. Probably a mild load. I doubt that the revolver has had more than a few hundred rounds fired through it. It simply was not shot much. The action and barrel are in excellent condition.