Starting with "S":
* Swinging serenades
* Swinging sensations
* Swinging symphonies
* Swinging secrets
* Swinging stories
* Swinging smiles
Starting with "W":
* Wildly swinging
* Whimsical swinging
* Wondrous swinging
* Whistling and swinging
* Wonderful swinging
Other possibilities:
* Slippery swinging (could describe a slippery swing set)
* Silky swinging (could describe a smooth, graceful swing)
* Soulful swinging (for a swinging musical performance)
* Smooth swinging (describes a controlled swing)
* Steadfast swinging (for a consistent, rhythmic swing)
You can also use alliteration to describe the action of swinging:
* Swinging swiftly
* Swinging silently
* Swinging steadily
I hope this gives you some good ideas!