I assume you've checked out some of the published sources, such as Peter and Iona Opie's Lore and Language of School Children, Oxford University Press, and William Wells Newell's Games and Songs of American Children which was first published in 1883 (reprinted by Dover in 1963) which might well be the first example of published field-collected children's material in America. Edith Fowke's Sally Go Round the Sun colorfully presents some recent children's playground material gathered in Canada.

The Library of Congress Archive of Folk Culture produced an album of kid's material, too. I can't recall the title, off-hand, but they included a song, "Roaches No More," that I collected 33 years ago from some neat African-American girls from Harlem and Bedford-Stuyvesant.

Sandy