Hey I remember the Beans, beans are good for the heart, the more you eat the more you fart. It was very popular in York (UK) in the 1970s.

I liked rhymes that had hand gestures (no... nothing rude) like

Incey, wincey spider climbing up the spout
Down came the rain and washed the spider out
Out came the sun and dried up all the rain
Incey, wincey spider climbed the spout again

or by linking the fingers of both hands so the fingers rest on the palm of the opposite hand

Here's the lady's knives and forks

then keeping your fingers linked turn your hands over so your knuckles face upwards

Here's the lady's table

then bring both index fingers upwards so the finger tips touch, leaving all the other fingers interlinked

Here's the lady's looking glass

then bring both little fingers upwards so the finger tips touch and rocking hands from side to side

Here's the baby's cradle

A similar rhyme using interlinked fingers went

Here's the church
Here's the steeple
Open the doors
See all the people