For what it's worth, I believe that Hank Ballard's song "Annie Had a Baby" is one of the main sources for the African American children's movement rhyme "Pizza Pizza Daddy-o". That rhyme starts with the line "___ [a girl's name] had a baby".

See this YouTube clip from a 1967 film of young girls in Los Angeles, California chanting and performing movements to that rhyme and other rhymes:

http://www.youtube.com/watch?v=N2YodFqZ7nQ