There are three versions at The Online Dictionary of Playground Slang. Not very nice, but interesting.
-Joe Offer, who didn't talk like that or he'd get his mouth washed out-

Ching Chong Chinaman sitting on the grass,
Along came a bumblebee and stung him on his..
Ask no questions, tell no lies,
I saw a policeman doing up his...
flies are a nuisance, bugs are even worse,
And this is the end of my silly little verse.


Ching chong chinaman went to milk a cow.
Ching chong chinaman didn't know how.
Ching chong chinaman pulled the wrong tit.
Ching chong china man got covered in shit.



Chin chin chinaman bought a little shop
And all he sold was peppermint rock
He wee'd in a bottle and called it pop
Chin chin chinaman bought a little shop