Alicia Keys, already on board as a commercial producer of the upcoming Broadway play “Stick Fly,” will pen original music for the production.Keys’ stint on the creative team makes her eligible for a Tony nomination, although it’s not often play scores are included in the musical-dominated category of scores written for the theater. Still, in 2010, the music from two plays — including the Branford Marsalis-penned score for “Fences” — made the cut. Keys is part of a “Stick Fly” producing theam that includes Nelle Nugent, Samuel Nappi, Reuben Cannon, Sharon A. Carr/Patricia Klausner, Huntington Theater Company, Dan Frishwasser, Sarahbeth Grossman and Charles Salameno in association with Joseph Sirola and Eric Falkenstein. Lydia R. Diamond’s play, a regular on the regional circuit and making its Gotham bow this fall, begins previews Nov. 18 at the Cort Theater ahead of a Dec. 8 opening. Helmed by Kenny Leon (“Fences”), play centers on a wealthy black family’s weekend gathering on Martha’s Vineyard. Cast includes Dule Hill, Mekhi Phifer, Tracie Thoms, Ruben Santiago-Hudson, Condola Rashad and Rosie Benton.