A limited edition of the regular Red Ryder BB Gun with a compass in stock. This is a mint weapon that can do insane amounts of damage if your skills are sufficient.
A "Bob's Pre-owned Car Mart" special random encounter. Look in the boxes behind the locked door. Very rare to get in the first game. It refers to an event in Wasteland.
If the children patch has been installed (or you have an American version) a kid in shady sands should be carrying one (getting it will require you to kill the kids.)
One can also be found in a shelf of the Dark Water General Store in Junktown. Behind the locked door on the eastern side of the building, the lock can be picked at night with sufficient skill.
It can be acquired in the Sierra Army Depot. With sufficient science you can resurrect Dobbs who will quickly die as a consequence of the unfreezing process. He carries the LE BB gun. The gun merchant in the NCR bazaar will also occasionally have it in stock. The LE can also be found via a random event while traveling in the wasteland. It can be bought at San Francisco Chinatown at Red's 888 guns for 4700 $.
The Red Ryder BB gun is also a powerful weapon obtainable in Wasteland, the predecessor game to the Fallout series. In Highpool, the party has to fight the child whose dog (Rex) "was gunned down by vigilante Rangers," or it could be acquired via cheat.
The Red Ryder himself is another reference to the BB gun and Wasteland. He shows up to fight the Rangers in revenge should they murder the children making fun of them after falling into the river.