Nursery rhymes and songs/Round and Round the Garden

Palm variant

Round and round the garden, (Make circular pattern on child's palm)
Like a teddy bear, (Continue circling)
One step, two step, (Move finger as if taking two steps with your fingers)
Tickle you under there! (Tickle child's armpit)

Woman performs "Round and Round the Garden", palm variant.

Tummy variant

Round and round the garden, (Make circular pattern on child's tummy)
Like a teddy bear, (Continue circling)
One step, two step, (Move finger as if taking two steps with your fingers)
Tickle you under there! (Tickle child's armpit)

Woman performs "Round and Round the Garden", tummy variant. 

Elsewhere in the wikiverse

"Round and Round the Garden" on Wikipedia