Why not? Here are a couple of circus-related songs for kids. Neither of them are "Miss Mary Mack," nor do they feature elephants jumping over the fence, but your kids may enjoy 'em. In any case, watching them is free, unlike your local Cirque du Soleil show.
The first video comes from Mates of State with another song from TV show Yo Gabba Gabba!. It's called "Circus Town," and while the embedded video is merely an extended excerpt, it's fun enough to include here.
Mates of State - "Circus Town" (excerpt from Yo Gabba Gabba! [YouTube]
The second video is from family band (literally) Kitty Wolf with "Circus Song" off their album Jump the Tracks.
Kitty Wolf - "Circus Song" [YouTube]
And, hey, why not a bonus video from Ralph's World?
Ralph's World - "The Rhyming Circus" [YouTube]