My post above was to the guy who was complaining about there being so many posts. Here's the version I heard my mom sing when I was a kid. Found similar ones above, but nothing the same. This was in the late 30's. I guess she made up the parts that were not clear to her:

There lived in China a very great man.
His name was Chingerie Ching Chiann.
His head was large and his feet were small.
This Chinaman couldn't walk at all.

Chingerie Chingle My Golday.
Tiddle dee dee come happy may.
To be isky imy oh.
Scallopin wallopin Chineo.

The ladies from the very next town
Came up the hill to roll him down.
From head to food they all began
To tumble and toss this Chinaman.

Chorus again.
I think there were more verses but I can't remember them.