How is your sleep? How is your sleep at night. Is it restful? Do you feel like you need more sleep when you wake up in the morning. Do you have a tendency to fall asleep while watching tv or reading a book. If you do, it might be a sing of sleep apnea and not related to your dm. If so, see a sleep specialist. Also check your blood sugar when you are sleepy - if it is not low, then dm is not the reason.
Need experimentation. If you feel sleepy after a meal or find yourself taking a nap on the couch after eating, it may be because of your diabetes. You will need to do a bit of experimentation to find out the cause of your sleepiness, but it is possible to correct this simple problem.