Get a cheap plastic tub that's not too tall and a few inches bigger than your litter box, and put the litter box inside. The spilled litter will land in the bigger tub. You could even use just the lid if you wanted. I have big bunnies with big litter boxes, so I use an under bed storage box.
Some people buy or build a hay rack and install it beside the box instead of putting hay directly in the box. That way there's less hay in the box to be tracked out.
I don't know if a covered cat litter box would work for rabbits, as I've never tried one for rabbits. Maybe others could weigh in on whether it's a good idea. My buns love their upside down tubs with doors cut in them for hiding or sleeping.