Hi.  If I remember correctly, J. W. Jenkins and Sons was a name of a
very large piano dealership located in Kansas City MO.  The decal
bearing the name "J.W.Jenkins & Sons" usually appeared on the inside
top lid.  They are common in our area (Missouri).  I have seen Vose,
Meister, Neuman Bros., Schubert, and Brinkerhoff pianos with this
decal, straight pianos and players.

In addition, you can find stencil pianos also bearing that name.
Most were made by Lakeside/Cable-Nelson, but a few were made by
American Piano Company; that was the same plate as the Franklin and
Foster pianos.

Although most piano companies would not admit it, nearly all of them
built some really cheap uprights and players just for the dealers who,
in turn, would dream up their own name for the piano.  Most of these
names were spelled very closely to some of the better-known makes, for
example: "Steiger & Sons" (the real piano by that name was "Steger and
Sons").  Hope this helps.

Best Regards
Andy & Chris Taylor
Tempola Music Rolls
http://home.swbell.net/tempola/index.htm