The Folger is inaugurating a subscriber-only play-reading series Oct. 14, with "In a Coal Burning House" by Jeffrey Kinghorn. The play -- about an American survivor of a World War II prisoner-of-war camp and his family -- won a Foundation of the Dramatists Guild/CBS award last April and has been produced by the Salt Lake Acting Company. Kinghorn will be there, working on the play for two weeks before a second reading on Oct. 28. The readings will be in the Rehearsal Hall at Fourth and Independence at 8 p.m. and will be performed by local actors who aren't members of the resident company; they're being cast this week . . . Folger public relations assistant Mary Resing is leaving in a few weeks for Berlin, where she plans to write and to watch the local theater scene. The Show Goes On

Nancy Paris, who plays the Nazi Mandel in the Studio's production of "Playing for Time," was showing off the theater's new dressing room after the opening last Sunday when she stumbled off the bottom stair and sprained both ankles. She performed last Wednesday and the rest of the week in a wheelchair, a period chair the theater found at St. Elizabeth's. The real hero of the evening was 7-year-old Chad Brian Wain, who assimilated the changes necessitated by Paris' injury without a fluff, despite no rehearsal. Director Joy Zinoman said she would be deciding today or tomorrow whether Paris would have to be replaced by an understudy . . . There's a Good Explanation

In case you're wondering why Arena is calling its first production "The Good Person of Setzuan," instead of the more familiar "Good Woman . . .," it goes back to Bertolt Brecht's original title "Der Gute Mensch von Sezuan." In German, mensch means human being or individual as well as man, and when neuterized is a fairly obscure German vulgarity meaning "slut." However, that subtlety isn't possible in English. Since the play involves finding a good person in the world, it was felt that using "Woman" in the title focused on the heroine being a prostitute. Also, Arena is using the Ralph Manheim translation, with "Good Person," as opposed to the original Eric Bentley. Odds and Ends

The Ellington School of the Arts will open its new theater Oct. 25 with a fundraiser starring the Duke's son, Mercer, and granddaughter, dancer Mercedes Ellington. The public school, now in its 10th year, raises funds to augment its city funding. Lena Horne and Sir Oliver and Lady Marjory Wright are also among the honorary chairmen for the event, which is black tie and promises to attract a legion of Washington twinklies . . . The deadline for applying for a National Music Theater Institute scholarship is Oct. 31. For details, contact Alexander Aldrich at the institute, Kennedy Center, Washington, D.C. 20566 . . .

Six plays produced and written by members of Adventure Theater, the children's theater at Glen Echo Park, are being published as a collection by New Plays Inc. in Rowayton, Conn., next year. The firm specializes in publishing plays for young people, which is what the 33-year-old theater company does as well. Individual plays by company members have been published previously, but this is the first collection . . . American University's theater has been bounced by a new sports complex, so new quarters have been set up in the New Lecture Hall Auditorium. Barbara Tucker-Parker, formerly of the Folger, has become their costume shop manager and designer, and Steve Holliday, formerly of the Studio, has become technical director. Coming Attractions

"Great Messiah," a new gospel musical by Rickey Payton, will be performed at the New Bethel Church of God in Christ later this month. Call 829-1523 . . . Burl Ives will sing in the Kennedy Center next Sunday; it's a benefit for the Center's Alliance for Arts Education . . . "The Foreigner" reopens at Olney Theatre Tuesday. The cast and crew are dedicating the production to playwright Larry Shue, who died last week in a plane crash. . .