I remember a song I heard at summer camp in Canada in the 60s. Unthinkable that anyone would sing it now. Clearly of the same origin as many of the other songs mentioned here, but a little different.

"Once in China lived a man
Name was Chickeracka Chee Chi Cho
Arms were long and legs were short
Chinaman could walk nor snort."

And the chorus went something like:

"Hoke chickeracka cheek chickaloro
Bongo loro piggywiggy wango
Hoko poko hit 'im in the coco
Chitterbee chatterbee chee chi cho."

For some reason it really sticks in my head over 40 years later. In fact, I found this thread because it was running through my head today, so I googled "Once in China lived a man". Weird.