They're nice little hammer pumpguns from around WWI - I have a later hammerless Model 38 from the late 1920's.
Bob's Gun Parts lists several vintage Marlin buttplates, most for around $20, so while you may not get an exact replacement, any Marlin HR rifle BP from the era your rifle was made would be correct.
http://www.gun-parts.com/buttplates/
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