The producers of “Cheers Live on Stage,’’ the two-hour theatrical treatment of the celebrated NBC sitcom that kicks off a national tour at the Citi Shubert Theatre next month, announced the cast Thursday. The show, a two-act comedy adapted for the stage by writer Erik Forrest Jackson and directed by Matt Lenz, will star Grayson Powell as Sam Malone, the character made famous on TV by Ted Danson, Jillian Louis as Diane Chambers, who was played on the sitcom by Shelley Long, as well as Barry Pearl as Coach, Buzz Roddy as Cliff Clavin, Sarah Sirota as Carla, and Paul Vogt as Norm. “Cheers Live on Stage’’ will be at Citi Shubert Theatre from Sept. 9 to 18.