Hi, Littlmak,
I don't recall any connection with Remington. I think Meriden was associated with Sears, Roebuck, or at least made a lot of guns for them.
Meriden, IIRC, went out of business around 1915, and I know of no source for parts. Their guns were never expensive or of high quality, and I really doubt it would be worth spending much time or money trying to find parts or have them made except for something very simple, like a screw.
If the gun has a family history, it might make a good display gun.
Jim