We get asked all the time about storage. Actually in general, hiding your ceiling hook and storing your swing are very common questions and generally, show the concern people have with their inlaws or kids seeing their products or asking questions.
Well, the good thing is, most of them can be hidden very easily. Generally, for most swings, they fold pretty small, albeit a little awkwardly, and can slide under your bed. Or another better option is just to hang them in the back of your closet.
The Screamer Swing, Sling, Twist and Stand all include carrying bags that will help you in storing your swing.