You can use cool tea bags to get rid of your dark circles. Just make tea bags and put them in the refrigerator overnight and they are ready for use in the next morning. Lie down and put the cool tea bags under your eyes for 10-15 minutes. Then they will get rid of dark circles gradually.
I have the same problem with you. Now matter how good sleep I have, the dark circles are still there and I hate to makeup to cover them. Some chronic disease can also cause dark circles. So you need to see the doctor and find out the true reason that causes dark circles.