With family members who don't like their photo taken ever, I found that honesty and involvement on that person's terms really help.
My wife used to hate every photo of her, taken by anybody, any time. I found that discussing what I am trying to achieve - in detail - and involving her in what the final shot will look like and most of all where it will be used all helps. In other words, plan your shot with the person, sketch out what you're planning to do, why all the lights/tripod etc.
Then, let your subject reject some of the photos. If she/he rejects all of them, take some more.
After a couple of shoots, the shyness, fear, uninterested person will see that your photos are pretty good, that she/he can weed out the really bad ones and that the photos are NEVER posted anywhere without their knowledge and consent.