the children's counting-out rhyme is first attested 1855 as eeny meeny moany mite; form eene meenee mainee mo is attested from 1923. Another variation is eeny meeny tipty te.
Online Etymology Dictionary, © 2010 Douglas Harper
Examples from the Web for eeny
When you don't have that in mind when you're going solo, it's an eeny miney mo setup.10 Ways to Have a Baby
September 13, 2009
Why, they could eeny most walk ashore, come mornin, if she holds.A Singular Life
Elizabeth Stuart Phelps
There was one consolation for Grace and Eeny in their solitude.
"I thought you were practising your music, Eeny," said Grace.
"Yes, Eeny," she said; and Eeny came in, looking at her searchingly.
"Grace, I hope he won't leave it to you," said Eeny soberly.