Jo -

I was in my twenties before I found out that Eeeny meeny was a racist song in the original. All through my childhood, my friends and I used "catch a tiger by the toe" and never heard it any differently in all that time.

But I don't really think of it as a "counting" song, per se. It's a rhyme used for random selection. By "counting" songs I was referring to those songs that actually played a par in teaching children about numbers.

Even so, I wouldn't condsider the song One is the Loneliest Number to be a counting song, although I kind of think of the song In the Year 2525 as a sort of makes-you-think-about-math-just-a-bit kind of tune.