dear bel,
you have just opened a flood gate.. in my family, i am the repository for all these song. some are clapping songs, and some are jump rope songs, and some are counting out (deciding who is going to be it, in a game of tag) songs..
the have been compilations done for NY songs, but it was back in the early 70!

some NY (and Boston, baltimore, etc) street songs, are american varients of child ballads, with the same tunes, and only a few word changed.

Like

Miss Mary Mack, Mack, mack
with silver buttons all down her back, back,
(many verses-- i'll think about them and write them down if you want)

Mary, mary, was your feet,
the board of health, across the street

this, the board of health, is an idiom for a Bof H nurse or social worker

Starting in a whisper, repeat, each time louder

Who put the overalls in Mrs Murphy's chowder?
If you won't answer, i'll ask a little louder!


a varient of a very old song.. it might even been a child ballad..

Miss lucy had a steam boat,
the steam boat had a bell
Miss lucy went to heaven,
the steam boat went to Hell--
O operater, give me number 9
i want to report a robbery,
He tried to steal my laundry
but all he got was a pile of shi--
(shi)ne your shoes and button

(and more- once i get started my siblings remember the parts i forget. It ends with some one falling some broken Glass.

My sistr had a baby,
she put him in the tub
He drank up all the water
He ate up all the soap
He died last night with a bubble in his throat.
Dead said the doctor,
dead said the nurse,
dead said the lady with the alligator purse!

the lady with the alligator purse=social worker

A Jump rope song, slow, then fast at the alphabet

Strawberry shortcake, cream on top,
My true love name starts on the letter i stop
A, B, C, ...

a counting out song...
Ink a bink,
a bottle of ink,
the cork fell out and you stink!

not because you're dirty
Not because you're clean
just because you kissed a girl
in a dirty magazine.