I'm going to attempt to answer this. The reason I hesitate is because Daisy have an unusual numbering system for their air guns.
Daisy made a no. 111 model 40 from 1940 to around 1966. it was part of the "Red Ryder" series. It was made in 8 variations. They also made a Model 111 "Western Carbine" from 1963-78 (I think this is your rifle) It's a 700 shot plastic stock rifle similar to a Red Ryder. They also made a model 111-B American youth in 1998.
One of these has to be your rifle