One of these days I'd like to poll the general public and find out what they think the word "by" means, with reference to music.

According to the catalogs of several libraries that contain the sheet music, the title is:

I'VE GOT A LOVELY BUNCH OF COCOANUTS (Note that this is not the standard spelling of "coconuts")
Words and music, Fred Heatherton, arranged by Johnny Warrington.
New York, N.Y.: Campbell Music, ©1949.

However, it also appears in several songbooks and recordings with the standard spelling:
I'VE GOT A LOVELY BUNCH OF COCONUTS