If someone is coeliac they would definitely need a gluten-free diet, which means no wheat, etc. If someone is diabetic they have to cut out sugars and cut down carbohydrates but there is still plenty to eat in addition to meat and vegetables. You can eat pulses (beans, lentils, etc.) You can eat rice so long as it is brown, dairy food so long as it is low fat, couscous, etc.. I have a friend in this position and he says he has no real problems and eats a full and varied diet.
What is not clear from your post is whether you have coeliac and diabetes, or whether you just wanted to know out of interest.