Meaning of nonny-nonny

non•ny-non•ny

Pronunciation: (non'ē-non'ē), [key]
— interj. Archaic.
  1. (used as a nonsense expression, esp. in Elizabethan songs and verses): with a hey nonny-nonny.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.