Depending upon which 'carbs' you are talking about. Veggies or bread/cake types??
Diabetes as you know is having too much sugar in the blood(unable to use it all as energy) which causes you to need more insulin or at the very least watch the sugar intake so you don't spike. If you don't use the sugar and over time your body has too much to process, it fills up it's stores of sugar and you get diabetes. (layman's terms). Unused sugar becomes fat but it also can become diabetes. So beyond exercise to burn energy it's on the diet. Sugars, breads, starchy foods, fruits (even potatoes, esp. sweet and yams...) turn to glucose the quickest in your body therefore increasing your blood sugar. If you want to slow that process, retard it in any way, then watch your entire sugar/starch/refined foods intake period!!
Here is a list of suggestions based on my studies(I'm studying nutrition) and although I'm not a doc I am using well-respected info as a guideline. You can recheck this and look at real statistics to see what works, not just the theory. Look at history of how people actually eat versus what some docs might have said about earlier guidelines, that may be outdated and inappropriate.
Veggies are good. And they are carbs. Especially the leafy greens(high in mins/prots), cruciferous(broccoli/cauliflower/brussel sprouts), asparagus, squash, lettuces, tomatoes, all kinds etc...
Lean meats are good like turkey, chicken, deep-water fish(limit due to heavy metals in ocean-research) and occasionally red meat which is high in saturated fat but ok at times. Nuts are good too and great for when your blood sugar drops and you need a quick healthy boost(macadamia, walnuts, peanuts, almonds@! and occ. cashews(high in sat. fat). Tofu and soy products are also good and yes they can be cooked to taste awesome! Just try! Protein slows down the digestion process which allows the body time to go through the metabolic process and bring sugar to the endocrine system slowly...as compared to actual sugar or bready-type foods which process the moment they are in your mouth(amylase is a carb enzyme that is in the mouth, breaking down food immediately). The longer food takes to break down to it's ultimate form, glucose, the more time your body has to cope with and distribute safely without spiking your blood sugar.
SO, again, carbs is a big vague word. Avoid processed foods like cakes, crackers, breads and instant rices/pastas. No sugary sweets especially with pure white sugar. Eat mostly veggies, meat, lean cheeses and WHOLE grains that have high fiber(not processed cereals and such) that also require the body more time to break them down(quinoa(high protein grain), brown rice, amaranth, Irish oatmeal... etc...) Whole grains mean you really have to cook them, they are not processed and in a box with 2 min. instructions. Once in a blue moon is okay, perhaps with a pile of Thai veggies on top!! yum...
The more processed, the less your body has to break them down, the quicker the sugar is released the faster your blood spikes!!
So get slow food....process slow and then digest slow. Ultimately slowing your blood sugar spike.
If you have to have a sweet, dulce as they say in latin. Try something fruit-juice sweetened and eat it around another protein rich meal so that your body is not bombarded with a hit of sugar alone. Or try an apple with a big dollup of peanut or almond or hazelnut butter on it...yum!! It really will taste good and your body will appreciate it.