Here's a version I used in a preschool in the 1990's. It is another non-confrontational, non-racial example of this rhyme. I used this "singing game" because the preschool was predominately black and I identified this as a culturally relevant game.

Down Down Baby

Down down baby, down by the roller coaster (shimmy shoulders and arms)
Sweet sweet baby, I'll never let you go. (hug yourself)

Shimmy shimmy co-coa pop, (hands on hips and shimmy hips)
Shimmy shimmy bop! (hands on hips and shimmy hips)
Shimmy shimmy co-coa pop, (hands on hips and shimmy hips)
Shimmy shimmy bop! (hands on hips and shimmy hips)

Grandma, Grandma-ma, sick in bed, (spread hands)
Called the doctor and the doctor said: (while mimicing a phone call)

Let's get the rhythm of the head--ding dong,
(rock the head to each side like a bell clapper in time with "ding-dong" with hands on hips)
Let's get the rhythm of the head--ding dong,
(rock the head to each side like a bell clapper in time with "ding-dong" with hands on hips)
Let's get the rhythm of the hands--clap, clap, (followed by two hand claps)
Let's get the rhythm of the hands--clap, clap, (followed by two hand claps)
Let's get the rhythm of the feet--stomp, stomp, (stomp feet; first right foot, then left)
Let's get the rhythm of the feet--stomp, stomp. (stomp feet; first right foot, then left)

Put it all together and what do you get?

Ding dong! (rock head)
Clap clap! (two hand claps)
Stomp stomp! (stomp feet)

Say it all backward and what do you get?

Stomp stomp! (stomp feet)
Clap clap! (two hand claps)
Ding dong!(rock head)