Dear WW: I can't remember now where I got the information
that "nonage" meant "ninth year". Webster 1913 doesn't support it:

Webster's 1913 Dictionary

Definition: \Non"age\, n. [LL. nonagium, from L. nonus ninth, novem
nine.] (Eccl.)
The ninth part of movable goods, formerly payable to the
clergy on the death of persons in their parishes. --Mozley &
W.


\Non"age\, n. [Pref. non- + age.]
Time of life before a person becomes of age; legal
immaturity; minority.

The human mind . . . was still in its nonage.
--Coleridge