My little sister is ten and they have a modified version of Take a peach rhyme:

they call me
eeny meeny
teeny weeny
ooh ah thumbalini
ah chi pachi liverini
i hate you

no peach
no plum
no stick of bubble gum
no peach
no plum
no stick of bubble gum

last night
i saw you with my boyfriend
how do i know
looked through the window
nosy
didnt take a shower
stinky
didn't do the dishes
lazy
jumped through the window
must be crazy

that's why they call me
eeny meeny
teeny weeny
ooh ah thumbalini
ah chi pachi liverini
i hate you