Hmmm, I thought you meant swing music and was going to suggest some 30's-40's ideas. Swing set/playground sounds a little child's birthday party to me. Other than including some photos in a collage or slide show, my inclination would be to do something a bit more sophisticated. However, that's me. If you really love the playground idea, I imagine you can get little toys to add to your decor at a children's toy or party store. You could do a groom's cake with a swing set on it--bakers can add a photo of just about anything to a cake. You could, possibly, even hold your wedding in a park, if that's your choice.
Like Myra, I thought of swing music, too, when I saw your post.
Sometimes when a person thinks of a theme for a party, they imagine that theme on everything. I have a mental picture of some kind of playground swing graphic on each and every item associated with your wedding: stationery, centerpieces, decorations, etc.
I suggest you scale that down. You don't want your wedding to be mistaken for a children's party.
I suggest you use the swing in one place only: On the cake. Wedding cakes are whimsical, anyway, so little bride and groom figureines in a swing at the tope of the wedding cake would look cute. As you cut the cake, say a few words about the significance of the swing.
That would be in good taste, IMHO. People would get the idea, have a little chuckle, then move on.