My mother also used to quote this ryme when she was trying to be funny.  She was born in 1908 in Mitchel, IN but grew up on a homestead in Othello, WA.  I agree with KatieJ that it was "Ninny on you tintype".  My mother would say it real fast, like a toung twister. 

Here is a slightly unrelated question. I did a search for Ice-breakers by Edna Geister and found it at Amazon with a sample of a few pages. On the first page I saw the word "ehaperone."  I immediately thought this was a typo of "chaperone" because "chaperone" fit well in the context.  But as I read further I found "ehaperone" used two more times on the first page.  I then did a search for "ehaperone" and found five hits on Google.  Each was in a newspaper and in each one I would have suspected a typo if it were the only time I had come across this word. Here is the question: Is "ehaperone" really a word? I've never heard of it. Or am I just continually uncovering typos?

Good eyes Ron. I was puzzled about where that "ehaperone" came from. I concur it was likely an OCR error. I use OCR on occasion, and see those errors all the time. In another font, it could have "ohaperone" or "chaperorre." Dick is indeed uncovering typos, but not the usual anthropomorphic ones. Then again, maybe we can fault the programmers.  :)