Tillysmummy, How awful for you. I was bulimic over 10 years ago and I agree with winnie1 that she needs to acknowledge that she has a problem. Unless she does this, no amount of treatment, books, websites will help her. I had, and still have, a very supportive network of relatives, friends and work-mates who tried to tell me that I was ill but I was in denial.
It was actually a stranger that spurred me on to get help before I killed myself. I had a burglary and Victim Support visited me. I don't know why but I just blurted out everything about my life and how I saw myself as "fat" (despite being 5 and half stone).
She asked me if I had been to the doctors and I said I saw no point as there was nothing wrong. She told me to ring up, request a lady doctor and, most importantly, request a long appointment (30 minutes, if possible). She then said to write down everything that I was unhappy with and wanted to discuss with the Doctor and take it to me to the appointment. I really didn't want to do it but I pushed myself to see the Doctor. I felt that I wasn't ill and I would be wasting the Doctor's time!
The Doctor was brilliant and told me that I had "Princess Di's Disease" and that she would refer me to a clinic and physciatrist. It was only when I was told that I had been allocated one of only 3 places in the whole of the borough that I realised I had a problem.
What followed was intense treatment followed by self-help groups for a year.
In my time I saw a few ladies in exactly your cousin's situation and some of them really didn't want to live. However, it does take time and there is no overnight solution. You need to learn how to love yourself before you can allow anyone else to love you.
In your cousins' situation this is going to be hard but I would really suggest trying to involve a third-party and spur her into helping herself. What about your cousin's sister making an appointment with her GP and explaining everything? The GP may be able to think of a way of getting your cousin into to see her.
I do wish you and your cousin every luck in trying to help her sister but it is not going to be easy.