Your best bet is to get Gerald Clarke's biography Capote. It's the full life, from someone who knew TC for about eight years, and portions of it are the basis for the recent movie. Capote covers the Answered Prayers fiasco at some length - TC started forming ideas for it before the Clutters were murdered, and was still talking about it as he lay dying in Joanne Carson's house. You really need the book to get all of it. Capote knew a TON of people and the book glosses the ones you need to know to get all the gossip.
I'll try to recap. TC intended Answered Prayers as a modern Remembrance of Things Past, the story of a poor man who rises to the glamorous top of society only to be disillusioned with the people he finds there. The narrator, PB Jones, is somewhat autobiographical. The heroine Kate McCloud is based on a lot of women, including Ann Woodward, Pamela Churchill, Cappy Badrutt, and the main one, Mrs Harrison Williams or "Marvelous Mona." The gossip Lady Coolbirth in "La Cote Basque" is Slim Hayward, later Slim Keith. "Cote Basque" names a lot of names too, including Babe Paley, Gloria Vanderbilt, and the Bouvier sisters, all of whom were familiars of TC. The "Kate McCloud" chapter includes Tennessee Williams as Mr Wallace, a gay john, Katherine Ann Porter as Alice Lee Langman, a sex-obsessed gossip columnist, and Ned Rorem, who is not disguised under an alias. A later unwritten chapter included a real-life male courtesan named Denham Fouts.
But it's the two main scandals in "Cote Basque" that were the bombshells. The first is the 1955 murder of playboy Bill Woodward by his wife Ann, who got off with the help of his mother Elsie. Ann Woodward committed suicide after reading an advance copy of "Cote Basque." The other is a wholly fictional account of how Bill Paley cheated on Babe with a menstruating woman and was nearly caught while washing the sheets in the bathtub. TC was close to the Paleys and his veiled swipe at Bill's philandering pretty well destroyed the friendship and the marriage. The public humiliation of Babe and Bill Paley and Elsie Woodward (no one liked Ann) cost TC most of his high society connections just as he was spiralling into alcoholism and drug addiction. This and the exhaustion from In Cold Blood wore him down to death.