Ford actually used a smaller V8, 136 cu. in. in the 30's. Found this.....may not have been "produced" by Ford at the time but was a Ford engine as much as the next one at that time due to the usage.
From wikipedia........
A 136 cu in (2.2 L) V8-74[3] version was introduced in the United States in 1937. With 2.6 by 3.2 in (66 by 81 mm) bore and stroke[3] and 6.6:1 compression, the engine was rated 60 hp (45 kW) and 94 lb·ft (127 N·m).[3] The designation changed again in 1939, to V8-922A, but the specifications remained the same.[3] It was produced in Europe in 1935 and 1936, and was used in the many standard Ford vehicles based on the car platform of the era. It was not very popular with U.S. buyers who were used to the 85 horsepower (63 kW) cars. Redesignated V8-82A in 1938, V8-922A in 1939, and V8-022A in 1940, compression, power, and torque remained unchanged.[3] The engine was very popular as a powerplant for midget race cars after World War II. This engine is most commonly referred to as the "60 horse" flathead, or the V8-60. It was replaced by the 226 straight-6 in the 1941 Fords.