I learned a version of this from my grandmother when I was little:

In Chinatown there lived a man
His name was Ring a ting a tang
His body was short, his leg were slim
Ollie ga wallie ga Chinaman

Chickara coo cha coo cha ra
Chack a roni made a pee olla pee
Olla pee dusk a China chew
Ollie ga wallie ga Chinaman

The Chinaman he lived in wealth
He lived in a mansion alll by himself
He sent his servant to Japan
To buy some tea for the china Man

Chickara coo cha coo cha ra
Chack a roni made a pee olla pee
Olla pee dusk a China chew
Ollie ga wallie ga Chinaman

The Chinaman well he did die
And in his coffin he did lie
The sent his body to Japan
And that was the end of the Chinaman