Found in the following dictionaries
SOWPODS (Collins Scrabble Words)
"Nonny" Definition
noun
A fool.
Source: Wiktionary
A meaningless word used in refrains, especially in old english ballads and glees.
Source: Wiktionary
A silly fellow; a ninny.
A ninny; a simpleton.
Source: Century Dictionary
A meaningless burden in old english ballads and glees, generally “hey, nonny.” it was similar to the fa, la of madrigals.
Source: Century Dictionary
A whim.
Source: Century Dictionary