Q, I suppose there may be no way of knowing, but it occurs to me that the children's rhyme "Down By The River Where The Green Grass Grows"* may have come from the "Down In The Valley Where The Violets Grow" {the lyrics posted in your 17 Sep 04 - 03:50 PM comment}.

*Also given as "Down In The Meadow Where The Green Grass Grows" and Down In The Valley Where The Green Grass Grows"

The words to that rhyme are given in Roger D. Abraham's "Jump Rope Rhymes, A Dictionary" {published for the American Folklore Society by the University of Texas Press 1969} as

Down by the river {in the meadow, valley}
Where the green grass groes.
There sat {any girl's name}
As pretty as a rose.
She sang, she sang,
She sang herself to sleep,
And up came {any boy's name}
And kissed her on the cheek.

-snip-

Abraham notes that this was originally a singing game. He cites a long list of publication of this rhyme, the earliest one being Babcock, W.H, in 1888 from the District of Columbia.

I remember a slightly different version {Atlantic City, New Jersey, 1950s}:

Down in the meadow
Where the green grass groes.
There sat {any girl's name}
As pretty as a rose.
She sang, she sang,
She sang herself so sweet,
Along came {any boy's name}
And kissed her on the cheek.
How many kisses did she get?
Ah 1, ah 2, ah 3 etc {jumper keeps counting till she misses. The number of jumps she made is the number of kisses she will receive {did receive}.

**
http://www.funjoint.com/outdoors.htm gives this similar version:


Down in the Valley Where the Green Grass Grows - - (... plug in name of jumper and favorite boy or girl "crush" of the jumper for the two names).

Down in the valley where the green grass grows
There sat Sally as pretty as a rose,
Along came Jimmy who kissed her on the cheek
How many kisses did she get this week?
1, 2, 3, 4, 5 etc. (jumper keeps jumping and counting until missing)

**

And I'm sure there are a number of other versions of this jump rope rhyme.