Something like this, maybe?
Tweedly-dee, tweedly-dee, Your breath stinks!
Rock in the treetops, all day long
Rockin’ and a-boppin and a-singin’ that song.
All the little birds on jaybird street
Love to hear the song go tweet, tweet, tweet!
Rockin’ Robin, tweet, tweedle-dee
Rockin’ Robin, tweet, tweet, your breath stinks!
I remember most of the one in the “Stay Soft Fro” TV commercial from the 70s (80s?):
That was about as close as I ever got to jumping rope and reciting a rhyme.
Did you got to school with me??? That’s exactly how we sang it, too, and I was just about to post and mention it!
We had another one (man, these are weird):
“I went to a Chinese bakery to buy a loaf of bread
he wrapped it in a pom-pom bag and this is what he said:
My…name…is…
Kay-I-pickle-I-pickle-I-kay-i
Wally-wally-whiskey
Chinese-pork-chop, BOW-WOW!”
I had no idea what it meant then and I still don’t.
We did that too! We had another verse starting from there. . .
DARK is like a movie, a movie’s like a show
A show is like a TV set and that is all I know
I know my ma, I know I know my pa,
I know I know my sister with the 80 liter BRA!
We had all of those. It was a really long rhyme.
Being in an international school meant you got jumprope and hand-clapping rhymes from all over the place… I remember this Japanese one which always got me confused right in the beginning because the hand gestures were so complicated.
We had one called Teddy Bear, in which one person would jump in the middle and the others would recite what they would have to do:
Teddy bear, teddy bear, turn around (the jumper turns a full circle while jumping)
Teddy bear, teddy bear, touch the ground (touches the ground)
Teddy bear, teddy bear, reach up high (reaches up high)
Teddy bear, teddy bear, say goodbye.
(At this point, the jumper would yell “Goodbye” and run out from under the rope. Then they would go to the other side and re-enter to finish the rhyme as follows:)
Teddy bear, teddy bear, climb the stairs (jumps alternating feet, like climbing stairs)
Teddy bear, teddy bear, say your prayers (holds hands like praying)
Teddy bear, teddy bear, turn out the light (pulling on a light switch)
Teddy bear, teddy bear, say good night,
G-O-O-D-N-I-G-H-T! (after the T, the jumper runs out and it’s the next person’s turn)
There was also a Finnish hand-clapping rhyme to the tune of “Chirpy Chirpy Cheep Cheep” about a swallow and a nightingale, and another one called “Sissikko”, but they don’t really translate that well… “Sissikko”, at least, was mostly just barely-English garbling, which was pretty much the point.
We had a lot of the previously mentioned ones: Miss Mary Mack, the steamboat, Cinderella dressed in yellow, etc. We also had a four person hand-slapping game to Rockin’ Robin, with lyrics I all of a sudden am having a hard time remembering, but that went at least in part like this after the chorus:
Mama’s in the kitchen cooking rice
Daddy’s in the bedroom shooting dice
Brother’s in the jailhouse raising hell
Sister’s on the corner selling fruit cocktail
Also we played Old Kentucky Fair, which may not be included in the scope of the OP, where a “senorita” stood in the middle of a circle, which went around her while she did motions that went with the song, and at the end closed her eyes and pointed and whoever she pointed at when “STOP!” came was the next senorita. Lather, rinse, repeat.
I went to Old Kentucky
The Old Kentucky fair
I met a senorita
With flowers in her hair
Shake it, senorita!
Shake it if you can!
Shake it like a milkshake
And do the best you can!
Rumble to the bottom
Rumble to the top
Turn around and turn around until I holler stop!
S-T-O-P STOP!
Does anyone remember “Slide”?
Sliiiiiiiiiiiiiiiiiiiiiide
Baby one, baby two…*
And that was it.
Down in the valley
Where the green grass grows
There sat (kid in the jumprope’s name here)
Sweet as a rose.
Along came (name of boy jumper has crush on-or perfect teasing moment)
and-
And I can’t remember the rest of it!
sorry.
:slinks away:
We did miss mary mack, and the hello operator one, as well.
Inka-binka-bottle of ink,
I think you stink!
Not because your dirty,
not because your clean.
Just becasue you kissed a girl behind a magazine!
Eenie-Menie-Miney-Moe,
Catch a tiger by the toe.
If he hollers let him go.
My mother said to pick the very best one and you are noooooooooot it!
There’s probably a dividing line (somewhere in the 1960’s) when kids started to “catch a tiger by the toe” instead of “catch a nigger by the toe”.
You can always avoid the entire controversy by doing
One potato, two potato, three potato four
Five potato, six potato, seven potato more.
Holy cow, I think I just had my first flashback! We did that one, too, (or something so similar as to make no difference) and I’d totally forgotten it.
We always did “Catch a monkey by the toe.”
Was “monkey” just a…nicer racial slur than “nigger”? I was about 25 years old before I even made an association between the two when I heard someone use “monkey” as a racial slur.
we used one of those lines in this one:
apples on a stick just make me sick
make my heart go two forrrrrty six
not because they’re dirty, not because they’re clean
not because you kissed a boy behind a magazine
heyyyyyyy, girls! wanna have some fun?
here comes Johnny with his pants undone
he can wiggle, he can waddle, he can do the splits
but I betcha 5 dollars he can’t do this!
followed by more hand-clapping, and I think you counted until someone fucked up.
Odd that this topic popped up. I was just trying to remember a double dutch rhyme that the girls in my neighborhood used to sing. It began “All in together” and that’s all I remember.
There was also “Numbers.” It was a two person clapping game. It started by clapping one’s hands together. Then right to right, then clap, then left to left, then clap again. Next slap the backs of the hands together, then the front, then start again. When you get to the back-front thing again do it twice. When you get to it the third time do it three times and so on. Its’ kinda hard to explain without demonstrating it. Anybody know what I’m talking about?
For two jumpers, two rope twirlers —
Singing telegram arriving
Calling Nancy at the door
<Nancy hops in alongside Susan>
Nancy is the one
Who’s having all the fun
So we don’t need Susan any more
<Susan hops out>
Hand-clap game — start with hands on our respective knees, my hands (and your hands) clap together on first word “my”, then my left claps your right on first syllable “ma”, then my hands (and your hands) clap together on second syllable “ma”, then my right claps your left on “told”, then clap our respective knees (nothing sung, “told” lasts for two claps), then my hands (and your hands) clap for “me”, which lasts while my left claps your right and then my right claps your left — then start over for the next line. I’m a little fuzzy about the exact wording of some of the lines, it’s been awhile since 3rd grade!
My Mama told me
If I was good
She’d buy me a dolly
Not made of wood
A rubber dolly
With a red hood
She joined the Army
She went to war
I haven’t seen her
Since I was four
I miss my Mama
Forevermore
The Army called me
On the telephone
My Mama died there
I’m all alone
And I got no dolly
To call my own
Hey, I know that one was a little dark, but I didn’t expect to shut down the thread with it!
Yeah, if you need us we’ll all be in the corner slitting our wrists. 
I just remembered, I saw a couple of kids doing something kind of neat with plastic cups a couple of years back. I don’t remember if there was a rhyme that went with it or not, but they sat on the floor facing each other, each one with two plastic cups in front of them. They then went through a complicated pattern involving handclapping and picking the cups up, flipping them over, and slapping them back down. Sound familiar to anyone?
I don’t remember one to Rock around the Clock, but I do remember it like this
Have everyone stand in a circle. Everyone stands with both palms up; your left palm on TOP of your neighbour’s right palm. At the beginning of the song, the leader slaps her left palm down on her right-hand neighbour’s left palm. This second person then repeats the action with her right-hand neighbour, etc., all around the circle.
The goal is to NOT get your palm slapped at the end of the verse. When the countdown gets to “FIVE”, if the girl who would get her left hand slapped by her neighbour at “FIVE” moves her hand out of the way in time, the girl doing the slapping is out. If on the other hand the girl doesn’t get her hand out of the way, she is out. Whoever is out moves to stand in the middle of the circle. Once several rounds have been played and you have three or four people standing in the middle of the circle, they can begin their own smaller circle and keep playing! The more players you have, the more concentric circles you can get.
Stella ella ola, clap clap clap
Say yes, chicko chicko, chicko chicko chak!
Say yes, chicko, chicko, allo, allo
Allo allo allo!
Say one, two three four, FIVE!
A clapping game I don’t see mentioned – Say, say, oh playmate.
I also remember:
Down down baby, down by the roller coaster
Sweet sweet baby, mama’ll never let you go
Shimmy shimmy coco pop
Shimmy shimmy rock
Shimmy shimmy coco pop
Shimmy shimmy rock
I know there’s more to it, but I can’t recall how it goes.
The version of Down down baby that I know morphs into the Let’s get the rhythm of the hands song that KRC mentioned, and the intro is a variation of monstro’s Sliiiiiiide baby. I went to an excellent lecture by a music historian on this topic about two years ago, and I recall that she said that this was one of the oldest documented hand songs. A lot of them go way back but weren’t necessarily written down. The let’s get the rhythm of the hands lyrics go back to the mid-19th century island communities of former/freed/escaped slaves in South Carolina.
Being a child of the 70s, a lot of the other songs I remember instead tap into the rich tradition of Madison Avenue. My favorite hand clap game was to the Oreo cookie jingle
*Ice cold milk and an oreo cookie
They forever go together
what a classic combination … * etc.
It’s hard to describe the claps, but it was vertical more than horizontal – you and your partner reached toward each other as if you were going to shake hands, but instead of the palms of your hands meeting, you held the backs of your hands together, and you started the clapping going up and down, hand over hand.
We also had one that started with the Two all beef patties, special sauce etc but I can’t remember anything else.