Btw, I believe that nowadays the "Apple On A Stick rhyme" is usually performed as a handclap rhyme.

The first verse usually is:

Apple on a stick,
makes me sick.
Makes my tummy go 2 4 6.

-snip-

In "Jump Rope Rhymes, A Dictionary" {published for the American Folklore Society by the University of Texas Press, 1969}, editor Roger D. Abrahams gives this verse:

Apple on a stick
five cent a lick,
Every time I turn around
It makes me sick.

-snip-

Abrahams cites these sources for that verse:
Musick: HF, 7 {1949}, 11 [West Virginia]
Withers, {1948}, 63
Butler and Haley {1963}, n.p.

[Sorry, when I 'zeroxed' these pages years ago, I didn't think that the page with the code for the sources was important enough to copy]

**

The reference to "turn around" leads me to believe that this was a jumpe rope rhyme. It seems that a number of handclap rhymes started out as jump rope rhymes.

Maybe we can blame the Maytag man and other corporate makers of clothes dryer [machines] for causing jump ropes to be difficult to find if not absolutely obsolete.