B757 First Officer discovers during climb out that the rudder trim is not functioning. After some discussion with Maintenance and Dispatch the flight diverts to the nearest suitable alternate.

Narrative

I was pilot flying. After take-off and during climb out; I noticed that the rudder trim was not working properly. It seemed frozen and when I looked down at the indicator; the needle (nor the rudder pedals) would move when I twisted the rudder knob. The aircraft was in trim; so I waited a minute or so before I tried to use the trim knob again. When it didn't work the second time and the Captain was not busy with his pilot not flying duties; I mentioned to him that there was a problem with the rudder trim. Since the aircraft was mostly in trim and flying well we had time to discuss and contemplate the situation. The Captain got out the Flight Manual but was unable to find guidance in this matter. He then asked for a phone patch to speak with Dispatch and Maintenance. I put the autopilot on and took over the ATC communications. We continued to fly outbound as he worked with Maintenance and Dispatch to try to solve the rudder problem. They were unable to solve the problem and so we decided to divert to ZZZ. The Dispatcher sent us our landing performance data over ACARS. The Captain declared an emergency; dealt with the Flight Attendants and made a passenger announcement. He then took over as pilot flying and I began the pilot not flying duties of preparing for the approach by loading the FMC; checking on landing weight and speeds for our landing at ZZZ. We advised ATC that we wanted Runway XXL as it was 12;000 FT long and had an ILS approach. We also advised them that we would be unable to hold short due to our heavy landing weight. Because of our heavy landing weight; potential rudder problem and gusting winds at the airport; the Captain requested emergency equipment to be standing by.