The counting out/choosing 'it' rhyme we used most often at primary school (East Lothian, early eighties) was

Ittle ottle, black bottle, ittle ottle out
If you want a piece and jam, you must walk on out.

We had 'Eeny meeny miney mo' with tigger not tiger (and squeals not hollers), again I had no idea it used to be nigger until I was much older. I do remember using the rhyme that Greg first asked about but I can't remember the first bit, just the 'icker acker dominacker rum pum push' bit. We also had 'Eenty teenty tether methera...' which went up to ten but I forget the rest...