Before World War 2, Japan's civil aircraft registration code was "J". The specific aircraft would then have a 4 letter code after the registration code.
As was customary at the time, the registration code would be painted on each side of the fuselage and on the tops and bottoms of the wings. Registration codes on the fuselage would have been moderate sized. Registration codes on the wings would be large and sometimes scaled to fit the wing's shape.
For example, the Japanese Ki-15 Kiragane "Kamikaze" which made a record-breaking flight in 1937 had the code, J-BAAI.
http://en.wikipedia.org/wiki/Aircraft_registrationI have no idea if there were any legal restrictions on what letters could be used after the country code, but not all letters of the alphabet appear to have been used. Most registrations are J-A... and J-B... but there's also J-C..., J-K..., J-T... and a few others.
Also, it appears to be very common, perhaps even law, for the "J" country code to be repeated on the plane's tail and/or tailplane.
Sometimes the "J" on the tail would be in a larger font.
While civil aircraft could be any color, there seems to have been a strong preference for mostly, or entirely, bare metal/silver dope surfaces. Some civil planes also carry the military "rising sun" roundels or had a variation of the Japanese naval ensign (the "rising sun" with red rays of light) painted on the wings. Again, I have no idea what the customs or laws were regarding such markings.
My guess is that a Tiger Moth with a J-A... or J-B... registration code, "J" markings on the tail and tailplanes, and a mostly bare metal/silver dope finish would be just about right for the period. If it had some sort of government function, or was flying into harm's way, then it might have also carried the national markings on the wings.
Links with pictures:
http://en.wikipedia.org/wiki/Kamikaze_%281937_aircraft%29http://www.straggleresearch.com/2010/05/some-japanese-civil-aviation-types.htmlhttp://www42.tok2.com/home/avionroad/Japanese%20Civil.html