Red Ryder was a pre-War air gun manufacturing company.
While many weapons in the Fallout universe are based on real weapons, Daisy's products are among the few real world weapons to be used in canon games. Much of Fallout's ambient graphic art is strongly influenced by this type of advertising. The Sugar Bombs box art and the Vault Boy campaign are among the most prominent examples of this.
The Red Ryder is mentioned in Fallout.
The Red Ryder BB gun is a real world weapon that was most famously referenced in the film "A Christmas Story." The protagonist wanted one for Christmas and was told repeatedly, "You'll shoot your eye out."