Just discovered what is probably the original version of this song with the songwriting credits. From:

http://lyricsplayground.com/alpha/songs/i/illneverletyoucry.shtml


I'LL NEVER LET YOU CRY
From the film "In Old Chicago" (1937)
(Music: Lew Pollack / Lyrics: Sidney D. Mitchell)

Versions recorded by Alice Faye (Film Soundtrack) - 1937; Teddy Grace - 1937; Artie Shaw & His Rhythm Makers - 1938; Slim Whitman.


A version by the Texas Wanderers (which has the pretty much the same melody I know) can be heard on Youtube at:

http://www.youtube.com/watch?v=WzWIs04inVo


One can conclude that the lyrics I posted above are a NZ verse added to the Pollack/Mitchell song. Cleveland's 1991 book has another quite different verse too.