When I was very young, my teacher Angeline Comorre, took out an autoharp and taught her whole third grade class "Supper on the Ground". The song was printed in our children's songbook, and had a picture of yes, people sitting at a picnic on the ground, with a checked tablecloth, and food, and someone was playing a guitar and folks were singing.

The words we learned then were similar to all the versions above:

"All the day a' singin', supper on the ground
Older folks and young'uns', gathered around
All your friend and neighbors, you surely will see
Come along Mary, and set by me" (It was SET and on SIT, colloquial I suppose)

Come along from Gloucester, and from Toxaway
Come here in the morning, stay here all day
Bring along your fiddle, your Pa's guitar too
Come along Mary, and set by me.

Bring your Ma's fried chicken, and some chocolate cake
bring vanilla pudding, all you can make
Every kind of vittle, you surely will see
Come along Mary, and set by me.
Come along Mary, and set by me.

One of the nicest songs I learned as a child. My family still sings it with guitar!