The Collaborative International Dictionary of English v.0.48:

Ninny \Nin"ny\, n.; pl. Ninnies. [Cf. It. ninno, ninna, a
   baby, Sp. ni[~n]o, ni[~n]a, child, infant, It. ninna, ninna
   nanna, lullably, prob. fr. ni, na, as used in singing a child
   to sleep.]
   A fool; a simpleton. --Shak.
   [1913 Webster]