We had a number of counting rhymes in the 70's.

[1]
We used: -
Eenie meenie minie mo
Catch a tiger/nigger by the toe
When he hollers, let him go
Eenie meenie minie mo.

We mostly said 'tiger', although 'nigger' was known of.
Incedentally, the word 'nigger' wasn't considered any more insulting than 'brummie', 'geordie' or 'scouse' are now.

[2]
Less well known, but more prized was: -
Eenie meenie mackeracker
rare rare dominacker
chicker packer lollipopper
om pom push
(the spelling is arbitrary!)

[3]
Quite popular was: -

Racing car number nine
Losing petrol all the time
How many gallons did it loose?

At this point the person whose 'spud' (i.e. fist) was counted on the word 'loose' would supply a number, say 'seven'. The rhyme was then completed using the supplied number, thus: -

One, two, three, four, five, six, seven
And out you must GO.

[4]
Later, we got lazy and the counting rhymes degenerated to this: -
Girl guide, boy scout, OUT.

[5]
And: -
Ittle ottle,
Shit in a bottle,
Ittle ottle,
OUT.

Nice, eh?