CSS doesn't have laundry facilities for guest use; however, if you really need something laundered they will do it for an additional fee. If you don't mind doing you own hand wash, most showers have a retractable clothes line that you can use. Just be aware that given the humidity it will take your clothes and your swim suits longer to dry.
At CSS there is also a laundry "special" - for $99 you can have unlimited laundry done by the resort all week. The special is not listed on the form, but is mentioned on a card in the room. They do a nice job.
And if you put the items out before 9am, they come back same day.