The Green grass grew around would work well - a cumulative song (with actions, possibly).

How about the Caterpillar song. To the tune of Coming round the Mountain. With more action. Not sure that I remember the words exactly. But each verse only has 1 line, repeated, and a spoken comment.
There's a tiny caterpillar on a leaf (wriggle, wriggle)
He's eating up the the leaf to make him grow (munch munch)
He spins a silk cocoon to take a sleep (spin, spin) [or something like that....]
Hes turned into a pretty butterfly (flap flap)