My Cinema 23-Inch HD Display (A1082) uses the Cinema HD DIsplay 90W Power adapter (A1097). If you go into any certified repair center (include apple stores) they should be able to order you a replacement.
Where ever you go make sure to have the serial number of the display, as well as the bad power adapter. The SN can be found under the stand. If your not 100% sure it's the power supply I would bring the display as well so they can test the display as well.
If you chose an apple store you would want to book an appointment for the Genius Bar.
http://www.apple.com/retail/geniusbar/