Actress Rosetta LeNoire will receive the fifth annual Richard L. Coe Award, it was announced Sunday. LeNoire has been active in theater for more than 45 years -- with Broadway credits including "Sophie," "The Sunshine Boys" and "You Can't Take It With You" -- and is founder and artistic director of New York's AMAS Repertory Theatre, a multiracial company devoted exclusively to the development of musical theater.

LeNoire is receiving the award for "extending the boundaries of theater," said Washington Post drama critic emeritus Richard L. Coe, the award's namesake and first recipient.

LeNoire, who also has appeared in numerous films and currently plays Mama on television's "Gimme a Break!," will be honored May 19 at a black-tie gala benefiting New Playwrights' Theatre. The ceremony, ordinarily held at the Kennedy Center, has moved this year to Ford's Theatre, where "Hot Mikado" is currently on stage. Not coincidentally, LeNoire's Broadway debut was in the 1939 Mike Todd production of "The Hot Mikado," which starred her godfather, Bill (Bojangles) Robinson.

Harry Belafonte, Colleen Dewhurst, Rosemary Harris, Ellis Rabb and Kitty Carlisle Hart, honorary cochairmen of the event, are tentatively scheduled to appear at the ceremony. Entertainment will include selections from Ford's production of "Hot Mikado" and appearances by Brock Peters and Martha Scott.Tickets cost $250, which includes a reception before the ceremony, the ceremony itself and a buffet afterward; $100 for the reception and ceremony; and $25 for the ceremony only. For information call 232-1122.$ Early Execution of 'Justice'?

"Execution of Justice," Emily Mann's docudrama about the trial of Dan White for the murder of two San Francisco officials, was a huge hit when produced at Arena Stage last spring, but it's not faring so well on Broadway. One critic, The New York Times' Mel Gussow, even singled out Douglas C. Wager's direction of the Washington production as superior. Wager, Arena's associate producing director, was to direct in New York but was replaced by Mann, who decided instead that she would direct.

Mortimer Caplin, coproducer of "Execution of Justice," said ticket sales in New York have been "tough." Caplin also said that after the play's mixed reviews, Mann had been persuaded to delete 8 1/2 minutes from her script "to tighten it up a little." 'Big River,' Flowing Into D.C.

The touring production of "Big River," the Broadway hit musical based on Mark Twain's "The Adventures of Huckleberry Finn," stops at the Kennedy Center April 23-May 24. The play, by William Hauptman and Roger Miller, won seven Tony Awards in 1985, including Best Musical and Best Featured Actor in a Musical for Ron Richardson, who will re-create his role of Jim at the Opera House. Brian Lane Green will make his musical theater debut as Huck. Benefit Booked for the Source

Joan Mondale is the honorary chair for a Source Theatre benefit to be held at the theater's two 14th Street stages April 15 at 6:30 p.m. Proceeds from the event, which includes cocktails, a buffet dinner, a silent art auction and scenes from "Beyond Therapy" and "Geography of a Horse Dreamer," will go toward the theater's resident acting company. Tickets cost $50; call 462-1073. Odds and Ends

New York theater producer Arthur Cantor will discuss his film "The Golden Age of Second Avenue" and Yiddish theater in general at a free screening and lecture tonight at 8 at the Jewish Community Center of Greater Washington; call 881-0100 . . .The New Arts Theatre will stage the American premiere of Irish playwright Graham Reid's "Dorothy," a drama that focuses on the conflict in Northern Ireland, Friday through May 3 at All Souls Unitarian Church . . . The Barter Players will bring their 1986 touring production of Neil Simon's "I Ought to Be in Pictures" to The Barns of Wolf Trap Friday and Saturday at 8 . . .

Opening this week: tonight, "Mama I Want to Sing" at the Warner Theatre; tomorrow, "Long Day's Journey Into Night" at the National Theatre, and Sanctuary Theatre's productions of "Bag Lady" and "The Orgy" at the Calvary United Methodist Church; Friday, "The Philadelphia Story" at Arena Stage.