It gets still more complicated. I have only heard "Two Lovely Black Eyes" played in 3/4 time. When we played it in the Russian bands, we played it in 3/4 time.

BUT

Someone gave me a DVD on British music halls for Xmas. And it showed some footage of an elderly Charles Coborn performing The Man who Broke the Bank at Monte Carlo and, of course, Two Lovely Black Eyes.

Oh, what a surprise! Coborn is performing it in 2/4 time!

It also shows footage of the sheet music, and that is written in 3/4 time.

Very strange.