The American Ford Roadster was never a two-seater, all had rumbleseats and button-on side windows. The last true (bright metal windshield frame) Roadster was 1936. 1937 had windshield frames as part of the cowl, and ended Roadsters altogether. All Open cars were DeLuxe since since 1934. The Convertible Coupe, with rumbleseat and roll-up windows, continued through 1939, the difference being the roll-up windows. Prior years with roll-up windows were called Cabriolets, going back to 1932, and Club Cabriolets having a back seat instead of a rumbleseat, starting in 1936. 1939 changed the Ford Club Cabriolet model to be a Mercury Convertible, coming back as a Ford again in 1940. The last 4 door Ford Convertible was 1939, The last Mercury 4 door Convertible was 1940, the last Ford Phaeton was 1938.
Whew! I think I got it all out there! I'll humbly request corrections from those who know better!