The South Shore Concert Band has done a series of albums called Sounds of the Circus, Volumes 1 through 16.

To find them, I recommend you go to AMG - All Music Guide, and then click on "Buy" which will take you to Barnes & Noble's website. There, you can click on the names of tunes and hear sound samples.

Barnes & Noble's own search engine won't find all these albums. I assume that's because they're not really currently available, but B&N still stores the information.

Another good album is Under the Big Top: 100 Years of Circus Music by the Great American Main St. Band.

Two tunes that sound like typical circus music to me are "Entry of the Gladiators" and "Thunder and Blazes."

Once you identify some tunes you like, you can use Google to find midi files (hopefully).