Oh, i remember that one fiber, in ny slightly different..

Say say oh playmate.............Oh my little playmate
Come out and play with me
And bring your dollies three
Climb up my apple tree
Slide down my {rainbow? rain barrel?}we'll sit on the lawn
Into my cellar door.................by the cellar door
And we'll be jolly friends...........best of friend
Forever more, more, three four.......more, more, more!

and it reminded me
Chose your partner, skip to my Lou
Chose your partner, skip to my Lou
Chose your partner, skip to my Lou
Skip to my Lou, my darling

skip, skip, skip to my lou
skip, skip, skip to my lou
skip, skip, skip to my lou
skip to my lou, my darling

Lost my partner, what should i do, (etc)

I'll get another one, prettier than you, (etc)

Flys in the sugar bowl, shoo, fly shoo, (etc)
red is the burden/chorus, and is repeated..
there are hundreds of verses.. i am sure others here will remember more..

and
When you get married
and your husband gets cross
Just pick up the broom
and ask, Who the boss?


and a spring time one
I have a little pussy
her coat is silver grey
she lives out in the meadow,
she stays there all the day
she'll always be a pussy,
she'll never be a cat
for she's a pussy willow,
now what do you think of that?


and
white coral bells, upon a slender stalk
lilys of the valley (mugets du bois)
deck my garden walk
Oh how i wish, that i could hear them ring
that will happen only when the fairy's sing!


and of course, we all sang and played (girls that is!)
London bridges falling down, falling down, falling down
London bridges falling down, My fair lady!

Take a key and lock her up, lock her up, lock her up (ect)

Get some money to build it up, build it up, build it up,(etc)

Still the bridge is half way down, half way down, half way down,[etc)

Some one go and tell the king, tell the king, tell the king (etc)

and many more verses..