This is the version I remembered from the mid 60s.

Chinaman had a wife, let her lead such a miserable life.
Led her up to the top of a hill.
Let her roll like a rolling mill.
Chicka lie chee chi cho chicka lora
Bunga lora piggy wiggy wack wack.
Hoka poka hit him in the coca.
Chatterby chatterby chee chi choka.

Chinaman had a daughter, let her play on the teeter tauter.
Led her up to the top of a hill, let her roll like a rolling mill.
Repeat Chicka....

I am sure a lot of words are wrong, but this is how I remember it. Sang it while jumping rope.