Tina is right, the Split is a good place to swim. If you are looking for the traditional beach, with soft sand, etc., that you will not find on CC. The sand is coral sand and packs somewhat hard. Sand has been brought into the area near the split- the one that has the palapas. I understand that bech chairs and loungers can be rented in this area.
Don't let the lack of a traditional beach keep you away from CC. It is a wonderful place to be and many things make up for the lack of soft sand. Wear sunglasses becaue the sand is so white it can be blinding, like snow (if you've ever seen that).