I learned a version of the 'Eeny Meeny rhyme' in school in the '70s on the Gower as a method of counting out. We used the version with the N word, but I don't think any of us actually knew what it meant, we just regarded it as just another nonsense word along with the rest of the rhyme.

We also had the 'one potato' rhyme but it was not used for counting out, it was more like a game in itself.

On another note, this is one that was around much later when I was a teenager and I've no idea where it comes from, it might have just been made up by the people who were chanting it.

I'll have a Degville Duckett
Duck it up and down
Bon Jovi, Cherry on a stick
I'll have a dry martini
shaken not stirred in a bidet
with a slice of lemon and two veg