After looking at the website, I saw the Crossman link and followed it.
If that truly is a Benjamin air rifle, it'll have a serial number on it which will indicate what year it was manufactured. There's a listing on the Crossman site.
If its a model 340, 342, or 347 it should have a serial number somewhere between
T298242 and T359568. That covers 1978 an 1979. I can't imagine they'd have used anything earlier than a year or two before since they probably didn't get the order for the props until a week or so before they had to play in front of the camera.
Model 340 is described as "Pneumatic, .177 cal. lead shot, single shot w/ under lever pump & checkered stock & fore end"
Model 342 is described as "Pneumatic, .22 cal. pellet, single shot w/ under lever pump & checkered stock & fore end (1st var.)"
Model 347 is described as "Pneumatic, .177 cal. pellet, single shot w/ under lever pump & checkered stock & fore end (1st var.)"
Maybe that'll help in the search?
-Gordon