You'll find the entire text of the story in Pete Seeger's book, Where Have All the Flowers Gone? - A Singalong Memoir. I won't post the story - Bettynh gave a link above to liner notes that have the entire text. But here's what Pete has to say about it in the "Flowers" book:

In a book of African folk tunes notated by J.N. Maselwa snd Rev. H.C.N. Smith, published (with no copyright of any sort) by St. Matthew's a missionary college in South Africa, I came across a lullaby. A footnote explained that it was sung as part of a story about a monster named Abiyoyo. "The parents get the giant dancing, and when it falls down in a fit, it is dispatched by the parents." From that hint, I improvised a new story for my own children, not realizing at the time how closely the symbolism hit home.
They wanted to hear the story the next night. And the next. I tried telling it to other kids at a summer camp, and acting it out more. Little did I know I'd tell the story, and sing the song, a thousand times in the next half century.

-Joe-