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Riverside Arms shotguns were made by Stevens. It should be close in design to the Stevens Model 94. There are no listings for parts for the Riverside single barrel, but the model 94 pin should be close. Numrich has them in stock.
What I usually do is make my own firing pins. .250 steel rod works. Turn an end down to fit the hole in the breech face, insert the rod into the receiver and mark overall length and where the retaining pin or screw goes and file out the groove for it. You will need to heat treat the metal when done. Heat it to bright orange, quench in oil and polish. Then heat to a blue-purple color and quench again.