Its obvious to me that it goes

Einie meanie macca racca
Rare Eye Dominacca
Chica Choca Lollipoppa
Rom Pom Push

MY mother taught it to me and she's always right

Though my dad taught me

Rim Strim Pimarickle
Leather Bone Ring Tale
Tim Tom Barny Kieno

He's from norfolk though so can be forgiven