NEW YORK — The private treasures of Frank Sinatra and his wife Barbara were a multi-million dollar hit at auction. Sotheby’s reported Friday that the couple’s entertainment memorabilia, art, jewelry, books and other personal items sold for $9.2 million — about twice their pre-sale estimates. A 20-carat diamond engagement ring that Frank Sinatra presented to his fiancee fetched nearly $1.7 million, surpassing a top $1.5 million estimate. “Frank tossed a bunch of diamonds on a bed and said, ‘Pick the one you want,'” Quig Bruning from Sotheby’s said last month, CBS New York reported. “Barbara picked the one she liked, she had it mounted in a ring. Frank gave it to her in a glass of champagne and she said, ‘Alright, you pick the finger to put it on.’ And that became her engagement ring.” Nine paintings by the legendary crooner also went for more than $850,000, against a high estimate of $120,00. Also up for sale was a Jewish skullcap with Frank’s name embroidered on it. It soared past a high estimate of $500, selling for more than $9,000. Some of the proceeds will benefit the Barbara Sinatra Children’s Center in Rancho Mirage, California, which counsels victims of physical, sexual and emotional abuse.