Ever since Richard Rodgers first saw Diahann perform he knew he wanted to work with her. He had her audition for the lead in Flower Drum Song in 1958, but they couldn't make her look oriental enough (as the role required). A few years later Mr. Rodgers saw her perform on the Jack Paar show, and he decided to contact Diahann again about a possible role in a musical. Diahann writes in her 1986 book, Diahann!: "The phone rang and a voice announced, 'Miss Carroll, Richard Rodgers is calling.' 'Of course he is,' I answered.'And this is Greta Garbo.'"   Soon enough Diahann was convinced it really was Mr. Rodgers, and they decided to meet the next day for lunch. This was the beginning of what would become No Strings. Mr. Rodgers actually had Diahann Carroll in mind from the beginning, and when they first met over that lunch, he hadn't yet actually written the musical, but wanted to see if Miss Carroll was interested in it before he went on conceiving it.   Richard Kiley was choosen for the male lead, Joe Layton became the director, and on Diahann's suggestion, Peter Matz was choosen as conductor. Ralph Burns wrote the arrangements. Diahann had a wonderful time during the rehersals. Layton was not only a gifted director, but also very good at negotiating - something you need when working with theater people... Richard Kiley and Diahann also had a very good working relationship. But when it was time for the first tryout (in Detroit) it was a fiasco. Diahann recalls in her book; "When we opened in Detroit it was our first night before a live audience. Once onstage, I must have blocked out everything except what I needed for the performance, and what I thought I needed was to perform as a singer, not a dancer. In any case, I concentrated so heavily on the singing that I did not take one single dance step the entire night. The dancers were very kind. Some of them grabbed the back of my coat and pulled me out of the way, then the others pushed me off to the side. It was so embarrassing, but I sold those songs!   "When the show was over, we all met downstairs in the lower lobby. I was mortified. I thought I'd never be able to live it down. 'What can I tell you, Joe [Layton, director]?' I asked him. 'Now you have positive proof that we don't all have rhythm.'"   The director then restaged the scenes so that Diahann only had to walk through them. But this was only a minor problem. More serious was the fact that they all had problems communicating with Richard Rodgers. Diahann was used to working with Harold Arlen, whom had been nothing but warm and friendly during her House of Flowers years. Richard Rodgers was totally different - according to Ms. Carroll he was much more formal, even insensitiv. Several incidents during these years made Diahann Carroll never to trust Richard Rodgers again. When Warner a couple of years later discussed making a movie of the musical, Mr. Rodgers did nothing when the movie company wanted to have an Eurasian actress named Nancy Kwan as the leading female. Diahann had to find this out reading the morning paper - needless to say she was furious. Mr. Rodgers said it was out of his hands, but Diahann never believed him. (NAACP ultimately protested against the lack of Black actors and actresses in Warner movies, and the movie project was shelved.)   No Strings opened in New York on March 15, 1962. Carroll and Kiley remained in the musical until July of 1963, for a total of 580 performances. During that time Diahann Carroll won the Tony for best actress in a musical (tying with Anna Maria Alberghetti in Carnival!), Rodgers won for best musical score, and Layton for his choreography.