I know yet another variation of "eena meena", which is this one (guessed spelling!):-

Eena meena mickeracka
Air eye dobinacka
Chickabacka chickabacka
Chinese choo-choo
Air-a-dona chickerona
Alla-balla wobstick
Out goes SHE!
Out goes another one and that is HE!

This was taught to me by my mother, who is now 91 and was brought up in Stockport (she's got a good memory!).

My brother (born 1945) always did "Dip dip dip, my blue ship" when his generation were picking "It", and at my school, we always did "one potato, two potato" (I was born in 1954, and brought up in Oxfordshire).

I also remember lots of other playground games and songs (such as "The big ship sailed on the alley, alley-oh") and skipping songs, using great long washing lines as the ropes, so lots of people could fit in - there were lots of songs which involved getting people in and out of the skipping group. A couple I remember are:-

Granny's in the kitchen
Doing a bit of knitting
IN comes a bogeyman
And pushes her OUT!

Matthew, Mark, Luke and John
The next person follow ON!

Do children still play like this today? (I don't have any so I don't know.) Nobody was allowed to stay indoors during 'playtime' in my day, you were pushed outside come rain or shine!