Here's a nice portal to search several different university archives for sheet music. For a lot of the songs published before 1923, you can look at and print the covers and inside pages if you want to try them out on your own piano.
Sheet Music Consortium
I remembered the talk of the early songs about Charlie Chaplin from 1915, and found Those Charlie Chaplin Feet here. Other Chaplin pieces include Funny Charlie Chaplin, also from 1915, and an Australian locally-published The Charlie Chaplin Two-Step and March, which does not have a copyright notice (though the archive has rather implausibly dated it to 1901-1910, which would surely predate the photo on the cover).
I also found that in the previous year, three songs were published about Mary Pickford (one of which, Sweetheart of Mine, may not actually be about her but claims to be her "official" song on the cover, no doubt as a last-minute attempt to cash in on a new trend).
Mary Pickford, the Darling of them All
Sweetheart of Mine
Everything related to researching, scoring and performing music with silent film.