The Crosman hollow black shoulder stock is model# 1399. It fits on 13xx, 22xx, and pretty much most of the pistols, I think, including the P-rod and the 1710T, and the Silhouette pistol, even. It retails for about $25.00.
I got one for my 13xx pistols. It works ok, but I didn't end up using it. The cheek weld is about the right height for using the iron sights. With optics, you might want to add an aftermarket riser. The gun is also a little more awkward to carry and to pump when sitting down, and the pistol grip is a little screwed up. The carbine also didn't want to set up against a wall or in a corner, unless I turned it muzzle down and backwards. Little things, but I just didn't like it, overall.
The 13xx is a fairly powerful, accurate, lightweight, compact air pistol. The 13xx carbine can be pretty powerful with mods, but it's really nothing special compared to a Sheridan or other high powered MPPs. I have a handy springer rifle that is only 1 or 2 inches longer than a 13xx carbine with a stock 10" pistol barrel and about the same power as my 1377 with 7 pumps; once I got my springer dialed in, the 13xx carbine was second-rate without spending another $100+ on it.
You will have to spend another $50.00 for a receiver if you want to properly mount a rifle scope. Another 45-55 for an extended barrel and barrel band.
That said, if you are a hunter or a low-volume shooter and you don't have a better rifle, for 25.00, the stock is a cheap way to instantly increase your field accuracy. But unless you go whole hog on your gun, I think a Crosman 2100 will blow it out of the water, ergonomically and power-wise, for only $60.00.