California Digital Newspaper Archives (which is really behind) has one newspaper reference to the Cotati team:

"The Tomales baseball team defeated the Cotati team at Cotati Sunday afternoon in the presence of a big crowd. The score was 17 to 8 in favor of the Tomales boys." (June 16, 1900, Sausalito Press) in your time frame. Searched 1890-1908

A gentleman named Walt Woolery is referenced as the "Cotati baseball manager"in the early 1900's. He also owned a pool hall/barber shop on LaPlaza Street shown here:
http://cotatihistoricalsociety.org/history-of-cotati

The historical society gives a pretty good overview of the towns history, may want to try to contact them for more information. Looks like they had a "renowned baseball team" in the 1920's (seemingly every small town did), and they built a huge, wooden racetrack for automobiles ("the same size as Indianapolis") in the 1920's. A two and half mile track in the middle of nowhere is hard to believe but.....
http://www.ci.cotati.ca.us/sections/...racetrack.html

Good luck, and GREAT PHOTO!