I borrowed this from Raffi, but wrote the last two verses myself.

Bumpin' up and down in my little red wagon

Bumpin' up and down in my little red wagon

Bumpin' up and down in my little red wagon

Won't you be my darling?

(Bump up and down)

The wheels turn around on my little red wagon

The wheels turn around on my little red wagon

The wheels turn around on my little red wagon

Won't you be my darling? 

(Turn your hands)

I'm waving to my friends in my little red wagon

I'm waving to my friends in my little red wagon

I'm waving to my friends in my little red wagon
Won't you be my darling?
(Wave)