Just like many state departments of transportation do, allow people to "Adopt a Station". They clean the station in exchange for a plaque with their name on it.
A lot of the ideas here are about cleaning the stations, a problem shared by many state highway systems. A solution some states have used is allowing people or organizations to adopt a section of the highway. They clean it in exchange for a sign, something like "This mile is proudly maintained by XYZ Company". A similar system could be used for stations. Hundreds of thousands of people use the Metro every day, the advertising potential of having your name displayed in a station should be an adequate incentive for organizations to sign up.