I learnt a variation on this 'song' from my father in Scotland in 1950. It was less overtly racist than most of those in this thread - it also had a punch line that I haven't come across in any of those I have read.

There lived in China, a long, long time ago a man with a long, long name. His name for short was: Chickaraka chickaraka chee chaye chang cho chocalorum malapaka wang oko toko idi kidi otiko idipi idipi chi yang fu.
And his name for long was Miles.