Have you tried oatmeal? I mean the real cooked kind, not instant. It has some carbs but it has a low glycemic index, which means that is digested very slowly. I have type II and I have found oatmeal to be a big help in keeping my blood sugar down.
Oats are often cross contaminated with wheat. I'm sure it's fine for folks who aren't gluten intolerant, but it does carry a finite risk for those who are.