I don't know if I can help you much, but I thought I would comment as I find this personally interesting. First, serial numbers were not required until after 1968 and the older gun makers didn't always (or ever) use them. Second, I don't know where or if you can find parts for it.
Thirdly, this is interesting to me because my grandfather had one of these. I was told he bought it at a farm auction for $2.00, perhaps sometime between 1910 and 1940 (dad always said a long time ago). Only gun that I knew granddad to have and he only used it to keep critters out of his hen house. Dad replaced the butt stock sometime in the '80s or '90s the stock that was always on it was stained (turned out after it broke) pine. Didn't realize it was pine till it did break and was not shaped like the original would have been. Yours looks to be original. Barrels on granddad's were nitro steel, can't tell from the pic if yours are steel or damascus.
Sorry I am not of more help.