We have fluorescent shop-light fixtures on a timer, and a rope light that comes on just before the fluorescents go off, and stays on for about 10 minutes, to give them enough light to go to bed. Just standard fluorescent tubes in them, and our birds kept laying all through the winter. We give them ~12 hours of light, though it's more so we will be able to see them when they're awake. We're away all day, so if we didn't supplement the light, they'd be asleep when we leave in the morning, and asleep when we get home in the evening.
Our winter coop is half the garage, so we have high ceilings to work with. For the short bunny hutch, a couple of rope lights might work. We like rope lights because they're all encased in plastic tubing, so if they peck nothing bad happens. You might even be able to find LED ropes with a solar power panel. I think I've seen those.