I'm not familiar with the term, and I can find no obvious definition online. But one can find a few uses of the term, and enough cases where "Ninny-Pinny" is used as a user ID to suggest that it's familiar to some group of people.
Some of the uses:
1 Ah, to be able to bring a pause to this whole mess, to the ninny-pinny men giving useless advice, to the bad news (to the endless briefings on the state of the economy and the ever-worstening crime in the streets).
2 "O Jo! how can you be such a ninny-pinny?"
(It should be noted that the above appears to be a quote from Alcott's Little Women, though I cannot locate the corresponding passage in the Google Books copy.)
3 At times, I feel a desperate need to write, but I fear that what I want to write most is from personal experience. Things that may scrape so close to the bone as to be painful to those I know and love and have no desire to wound. (And YES, I know that last sentence was a fragment, brain. Stop being a ninny pinny.) (Oh, for goodness' sake, now I'm looking up ninny pinny. I give up on me.)
The evidence suggests that the term is basically a sort of "rhyming slang" version of "ninny", which has already been defined above as a "foolish or stupid person". Very likely the appearance in Alcott's book (if indeed it did) gave what would have been a nonce term "legs" among the audience of Alcott's admirers.