The rifle is based on the Remco "Monkey Division" Okinawa toy rifle.
This is commonly know as the "chariot rifle". It was made and used in the Pilot. Then was used in the first season as well as the other version.
There is a third rifle, the third season version.
There may be some seasonal overlap on when each was first used. I've never seen any kind of definitive list showing when each was first used.