If the room is laminated or hardwood (like mine). I got the largest office chair protector plastic pads I could find. Put those in the corners under the litter boxes and it has worked out well. For the occasional accident off the pads a quick wipe and descent usually prevents repeats.
Lay down cheap vinyl sheet goods over the carpet. Get some cheap (as cheap as it gets) MDF moulding. Use finish nails to fasten the moulding to the existing stuff. Sheetrock screws will make too big a hole. The finish nails will leave a much smaller hole to fill. Run a bead of caulk along the bottom of the moulding before you set it in place and nail it to seal it to the vinyl so the pee and other liquids won't run under it.