Like P&R Fan said, Cowboy Loads are loaded with less powder, so they have less recoil. They aren't much good for distance shooting, but neither is a snub nosed revolver and under 25 yards they have about the same accuracy as full power rounds.
If you cannot find any locally, this is what my wife used before I figured out how to reload them for her.
.357 Magnum 158gr Rd. Nose Flat Pt. 1000pk
(They come in quantities 50 and 100 also.)
Great.....thanks for the info...will check it out.
As for cleaning, I'll probably get yelled at by other forum members, but I finish a range session by running a few FMJs through the guns I've been shooting lead through, give them a squirt of Kroil, CLP, or something similar and then I run a Bore-Snake though them while they're still warm followed by a wipe down with an oiled rag. At home I'll give them more thorough cleaning if they need it, but only if they need it.
As for the rings of powder residue that form right before the cylinder diameter reduces down to the throat diameter when you shoot .38spl in a .357mag, they aren't a problem unless they are thick enough to hamper loading and extracting .357mag ammo. I use oversized bore mops and brushes to keep the rings in my .357mag revolvers to a mild roar, but I never use steel bore brushes.
I took my gun to the gun supply store and they said the rings were ware and if I shop a few .357s thru it then they would disappear. Did that today and the rings are still there even after a thorough cleaning. Shooting seemed fine but extracting seemed a bit stickey in one chamber in particular. I also bruised the heck out of my hand. Tightened up my grip and it really helped but by then it was too late.....space between my thumb and index finger is purple. Ha ha......learned a lesson there. 
John