From the sound of the chords I would say the banjo is tuned CGBD. I think this is being played with a plectrum. According to the internet, which is always right (or maybe not), Joe Roberts was an early mentor to Roy Smeck. The latter is associated with tenor banjo (CGDE) so I am a bit corn-fused.
Also the recording quality is better than what I would expect from a cylinder recording. Is it possible to make a cylinder recording with microphones?
The recoeding is dated 1923, contemporary with Eddie Peabody (who got out of the Navy in '21 and went directly onstage). Peabody had a good run between wars, but the nostalgia boom of the 50's (Dixieland, etc.) put him on the map. E.P. put the banjo bug in my ears when I was a kid.
That has got to be a very late Edison cylinder pressing. They were phased out in the 20's, IIRC.