Have they got marks on them or are they just dusty? You could try this on one slat to start with: Talcum powder, either puff it on or brush on lightly with a clean, dry paint brush ( about as wide as the slat, leave for about half an hour. Brush off excess with dry brush and then Hoover using soft brush attachment. Or, if you have a steam cleaner maybe that would work, depends on if they are made from an absorbent material or not.
