Avoid sweets/starch. As a diabetic your father has difficulty clearing sugar from his blood. Simple sugars such as table sugar and the sugar in milk, fruits etc. Will raise the blood sugar level. Starches are simple sugars in long chains. When absorbed from the GI tract they increase blood sugar as well. Limiting these things will help control the blood sugar and may allow weight loss.
Sugar dense. There are no foods that can't be eaten by diabetics. That said, most people with diabetes should avoid sugar and carbohydrate dense foods which offer little nutrition. For example: donuts, bagels and similiar foods. This is not much different from the same foods that we should all eat in moderation.