You can make a "big top" cake with half-sphere pan (you know, like half of a ball) You can probably buy one at Michaels.
Decorate it with white icing. Use red licorice whips as the stripes going down the tent. Stick a multi-colored candy cane out the top to be the tent pole. Then cut a fruit roll-up to be the flag on the pole. Make a circle around the pole and along the base of the cake with big ball-type candy - like fruit sours, maybe. Then around the bottom half of the cake, make a line of animal crackers between the stripes (you would need to space the stripes wide enough for the animals to fit).
If you need a lot of cake due to a lot of kids, you could supplement with lion cupcakes - just make a mane around the circle of the cupcake with candy corns and draw a simple eyes, nose, mouth with brown icing.
As part of the party favors, don't forget the circus/animal crackers boxes.
Paint used vegetable cans in bright colors and use them to make the carnival can toss game (where you throw a ball at a pyramid of cans.
If you are considering a bouncy house, a friend of mine actually bought one brand new for much cheaper than cost of renting one. I also just looked on Craigslist for you and saw two different bouncy houses just posted yesterday for under $100 each.
Have fun.