I have several I-J and U.S. Revolver revolvers some were designed for black powder and some for modern propellents. I found some reasonably priced modern 32 S&W (short) ammo on line made by Remington. They are 88 grain lead round nose bullets that was manufactured fairly recently. As already posted, they're fun to shoot. The sound is more of a "pop" than a normal gun shot sound. Be careful about the bullets bouncing back at you. A friend had this happen when he fired close range at a 55 gallon steel drum. The bullet did not penetrate the side of the barrel and bounced back hitting the guy standing next to him. No one was injured, just scared sh**less. The cartridge was designed for card table range and to discourage would be attackers.
I've reloaded some of my cartridges using 32 ACP dies, 85 grain cast lead 32 cal bullets and 1.4 grains of W231 powder. Of course you could use BP instead. The older guns are always questionable and unless you know what you have it's advisable not shoot them. If it breaks open when fired and you get a face full of hot gas and the spent cartridge in your eye...
This place sells it look for Remington R32SW