My Grandma (Lancashire) taught my dad (now 82)
'Ar Rar Chickerah, chickerah rooney
Rooney pooney sting stong stiney
aragaraweskey chinese choo' as a counting or clapping game
My mum knows a version- she's from manchester.
I did read a version where 'aragara'was changed to 'albaster' in a story set in Wigan.
No help, but more info