Here is a rhyme that has in it a distinctly American twang:

Ena, mena, mina, mo,
Catch a niga by the toe,
When he hollers, let him go,
Ena, mena, mina, mo.

Here is another familiar jingle:

Anna, mana, mona, Mike,
Barcelona bona, strike;
Care, ware, frow, frack,
Hallico, ballico, we, wo, wack!
Huddy, goody, goo,
Out goes you!
Eatum, peatum, penny pie,
Babyloni, stickum stie,
Stand you out there by!

This is Irish:

A lirripeg, a larrapeg,
A bee, a nail, a stone, a stack,
A bonny Billie Gelpie,
A Belia-bug, a warum rock,
Crib-i-stery, Hick!

The little Turks and Armenians use this count: