I'm not connected with the Airline Industry but do have to deal with the public on a daily basis and have done most of my working life. I too often found it quite difficult to deal with angry and upset customers and decided to try and find a better way of dealing with things as I felt that my ability to deal with the situation in a more professional manner would probably help end the situation more amicably.
I did some reading and found 'Dale Carnegie - How to win friends and Influence people' one of the best books i've ever read and it not only helped me in my professional life but also in my personal life to. My wife thinks it ridiculous that I have to read about what she calls 'common sense' but that's perhaps because she's never read the book or others like it. I'd highly recommend the book to anybody who has to deal with people on a professional basis and in fact i've even bought it for some of my customers who have in turn read it and started to deal with situations in a much more positive way