Hi, I'm Aliza. I'm a Medical Librarian (retired) but still stay active in my field, working and helping people do research here and elsewhere. I'm also a BC patient. I have many people in my family who've had Colon Cancer (but none who had BC). It's very important to be screened and because there are so many people in my family who had this illness I was screened first at age 41, not 50.
I think one of the best things you can do to convince your family to get screened is to expose them to a celebrity that's familiar with the illness and the best one that comes to mind is Katie Couric, whose husband of many years unfortunately died from this illness. I found you an interview with her and Marlo Thomas that among other things covered this topic. It was in the Huffington Post. The URL for it is this: http://www.huffingtonpost.com/2012/03/16/colon-cancer-awareness-from-katie-couric_n_1354390.html.
But if you have anyone in your family Google "Katie Couric and colon cancer" (no quotations necessary when they search), they'll likely find a wealth of information that will stress the importance of getting screened.
I really think the celebrity theme is a big draw for people who are reluctant. I hope you find my advice helpful. If there is anything else I can do for you, don't hesitate to ask.