score:3
I wondered the same thing a few times so I looked it up: Eeny, meeny, miny, moe
I thought the original version was the one using the N word, actually the oldest known version (1815, New York) goes something like:
Hana, man, mona, mike;
Barcelona, bona, strike;
Hare, ware, frown, vanac;
Harrico, warico, we wo, wac.
It evolved into the more recognizable:
Eenie, Meenie, Tipsy, toe;
Olla bolla Domino,
Okka, Pokka dominocha,
Hy! Pon! Tush!
My knowledge of old English is non-existent and I wouldn't be able to tell you what those two versions mean. But they don't seem to be racist at first glance.
There's two common verses that come after the verse with the N word, in that version:
If he hollers let him go,
or
If he won't work then let him go
Unless the "let him go" implicitly means "kill him" it doesn't seem to be about lynching.
They were probably "innocent" verses for the people who would have sung that in those days. (Just to be sure I don't offend anyone I'm not saying they're innocent by today's expected moral standards.)