Spin it like a top

If you set it on its side so that one could see the sun through the hole in the middle from an orbit further out. then spin it around that axis, You'll have a day/night cycle similar to earth's. The outside will be normal, and the inside will have eclipses in the middle of each day.

Edit: Now that I think about it some more, the inside will spend most of their time in twilight. Either from the eclipse, or from all the light reflecting back at them from the ground "above" them.