Anyone ever mounted a scope on a Rem. Model 33 single shot rifle? A good friend wants it done to his squirrel gun. This old boy lives the life a lot of us wish for. He almost lives a subsistence life, eating mostly fish and game he harvests, and trades for nearly everything else. Says his eyes ain't as good as they were, so needs a scope. Lord only knows how many squirrels and other small game the gun has accounted for.
I think you will need to make the bases. Should/looks to be a round receiver so measure it. Drill that hole in some 3/4" thick or so aluminium plate say 2"x2". Cut it half, trim the sides so they don't interfere with the stock. I'd make sure the base is tall enough he can still load the rifle with the scope in place. You could drill and tap the bases (not in the center) in place or a glue like metal set on the receiver.
Get a Weaver flat one piece and D&T it to your base (on the other side of center. Mount scope of choice in Weaver rings, install on the rail.
You could do a lot of modeling with plastic and glue to work out the details.