Back about 50 years ago, my sister and I were in a Sunday School concert singing this song, dressed in blue gingham and with artificial plaits attached to the back of a tied-on sun bonnet. I can't remember who taught us the song but I remember it well.

Verse:
Once there lived side by side
Two little maids,
Used to dress just alike
Hair down in braids
Blue gingham pinafores
Stockings of red
Little sun bonnets tied
On each pretty head.
When school was over
Secrets they'd tell,
Whispering arm in arm
Down by the well.    (change key here)
One day a quarrel came,
Hot tears were shed.
You can't play in my yard!
But the other said:
chorus:
I don't want to play in your yard.....(see above)