Keep an extra sponge in your main tank's filter and transfer it to the hospital tank as needed. Voila- instant cycled tank! Return the sponge to the main tank when done or replace with a new one to be seeded for future use.
I just leave my hospital tanks running and throw one of my male bettas in there to keep it cycled. When I need it for my cichlids, the betta goes back in his bowl...Kind of like a mini vacation for him, and no empty tanks for me!
I leave my hospital/quarantine/fry tank in a box and empty until needed. Then I just take some media from the filter of one of my other tanks and place it in the hospital tank's filter and its ready to go.