Green’s Dictionary of Slang

cheap, second-rate; of a jazz musician, old-fashioned.

1928		W. Winchell Your Broadway & Mine 20 Nov. [synd. col.] [S]language [...] in use among musicians. [...] To refer to an instrumentalist as ‘corn-fed’ or ‘tinny’ is to term his jazz interpretations old style or ‘has been’.
1988		McGill Dict. of Kiwi Sl. 113/2: tinny [...] not very impressive; from tin being regarded as an inferior metal to iron or steel.
2003		McGill Reed Dict. of N.Z. Sl. [as cit. 1988].