R.B.
I have the exact same issue and I don't wear makeup either (never really learned how to do it well enough, so I stopped trying! lol!).
I've read lots of articles saying that allergies cause the dark circles, particularly since airborne allergies can cause itchy eyes, which causes you to rub them, which irritates the thin, sensitive skin and causes the dark circles. And quite frankly, since it's been going on this long, you probably don't even know you're doing it anymore! So, suggestion #1 is to find the source of the dark circles as opposed to merely covering them up. Claritin, Zyrtec or the like will likely help take away the itchy eyes.
Suggestion #2 comes from my sister who also gets circles, but tends to wear more makeup than I. She uses (and bought me) mineral powder: Physicians Formula brand Mineral Wear loose powder matched to your regular face skin tone. I do try to use it on special occasions or for pictures where I don't want to look like I got punched in the face. Just dab your finger in it and lightly dot around your eye and then *gently* blend in. Bonus is that you can also use it all over your face for a nice finished look--covers up any unsightly adult-pimples...I mean blemishes :) and it keeps away shiny spots.