When I was a kid we had an LP of songs recorded by the ABC in the 1950s or early 1960s which included this one. Being an official recording, the words are probably a cleaned up version of the street songs but it went like this:

One two three a-lairy
I saw little Mary
Sitting on a dromedary
Eating chocolate fishes

One two three a-lairy
I saw little Mary
Sitting on a missionary
Eating jelly babies

One two three a-lairy
My ball's down the airy
Don't forget to give it to Mary
Not to Charlie Chaplin