Find local performers to do a show; or put on circus act videos from youtube on the big screen or projector. Offer kids popcorn and/or peanuts as snacks. Bring out any birthday cakes after the videos/performance, then have a present opening ceremony once cake is done.
Facepainting – fit in with theme, especially animals. Hire a local facepainter, or learn it and/or balloon twisting on your own. Don’t worry about overcomplicated balloons; if you can learn just a few relevant shapes, then simply present the list of options to the kids. Animals are always popular, and silly hats are both fashionable for a circus and far less likely to pop.
Hula Hoops: Make sure every kid learns the basics of hula-hooping, then have a challenge to see which kid can hoop the longest. Then the winner can go first in the next game, which is to leap through the hoops like they’re the favorite animal of their choice.
Juggling: kids can practice throwing soft balls of any type by themselves or with each other; you can gather them in a giant circle, and give every kid one ball, and see if they can keep up with passing to each other in a random pattern. Then gather all the balls, and let kids take turns with their aim. Next, the kids can do a ball toss, either aiming for some cut-out holes, or to have their balls land inside of some hula-hoops from a fair distance.
Tightrope Walking: Fasten a long, thin piece of lumber against the ground, and have the kids take turns balancing on it. If this is too easy, make it a race, and see who can successfully make the walk in the shortest time.