The Red Ryder BB gun is a BB gun made by Daisy Outdoor Products and introduced in 1938 that resembles the Winchester rifle of Western movies. Named for the comic strip cowboy character Red Ryder, it is arguably the most famous BB gun in American history.
One can also be found in one of the shelves located inside a room in the Darkwaters General Store. The room is locked and you will need to pick it. Doing this right after telling Killian Darkwater that Gizmo hired you to kill him increases the chance of Killian not caring about the break-in. A dialogue may open; just play it cool. Killian will ask you to get outside of the room as soon as possible, so loot fast and he won't bother about you taking the items.
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.