There are many pull behind attachments made for lawn tractors (see Sears, Agri-Fab, Brinley). Most use a pin hitch (it's what you want for your tractor). Look to see if the back of your tactor has a tongue with a hole in it.

yank in va, I pull a plug aerator with my old STX-38, and have for years. My Deere is a 5-speed, not a hydro transmission. You attach the aerator with a pin, which will likely come with the aerator. You will likely find that you need to add some weight to the aerator tray; I use four concrete construction blocks and sometimes put a 40 lb bag of cement on top. If your STX is hydro, I wouldn't put the extra 40 lbs on it just to be on the safe side.