Coltex: I have a pretty good sized collection of old Conoco gas station photos. From what I can tell, your sign was used by Continental Oil at some dealer stations in the 1920's. Those signs would have been discontinued immediately after the merger between Continental Oil and Marland Oil in mid-1929. In the 1920's, the gas stations that were built and operated by Continental Oil tended to have a "Continental Oil" sign on the building, more in a rectangular shape than the rounded one you have. And I have seen lots of Continental Oil dealer stations that don't have that sign....so I don't know what the company policy was. I am attaching four of the best photos showing that same sign (I believe I can only attach four at a time). Let me know if you want to see more....I probably have a couple more.

Lehi, UT (Dean's Conoco) #1a in 1928 [FB Kurt Zimmerman].jpg Paris, AR (City Service Station) Continental station <Visible pumps> [Conoco Sentinel Magazine Jul 1928.jpeg Muskogee, OK (C. G. Kendrick) Continental station <Visible pumps> {CAN2} [Conoco Sentinel Magazine Apr 1927].jpeg Spanish Fork, UT (Checkerboard Service Station Cornish Brothers) Continental station <Visible ;pumps> [Conoco Sentinel Magazine Jul 1928.jpeg