Here are the variations I learned:

Cici my playmate
come out and play with me
and bring your dollies three
climb up my apple tree
Slide down my rainbow
into my cellar door
and we'll be jolly friends
forever more, 1 2 3 4.

The last line variation is common to a lot of these hand clapping games; counting is found replacing words all the time. Also, sliding down the rainbow is a newer concept, probably from the puff the magic dragon period of childhood learning, however it lends to a great line in the next song:

Cici my enemy,
come out and fight with me
and bring your handguns three
climb up my poison tree
Slide down my razor blade
into my dungeon door
and we'll be hateful enemies
forever more, 1 2 3 4