Carnival offers shore excursions for passengers with flights departing after 4:00 p.m. I don't have any particulars on them, though, because I had an earlier flight (just got off the Destiny Sunday, November 16).
I think they have a rainforest tour and a "relax at the pool" type tour that you can take if you have a late flight out of San Juan. Your luggage will stay with you the whole time. There isn't anything to do (or eat) at the San Juan airport so don't plan on sitting around there. You will be bored out of your mind.