Hammock or Porch Swing
Inspired by the swing set I built many moons ago, this is perhaps slightly less hokey, and maybe even more fun. The idea is to create the classic scene with two trees and a hammock hung between them. It would be an ideal application for a crank, with the only tricky part being to decide how to connect the mechanism to the hammock: it could be simply a wire out the back of a tree and into a building, or a miniature crank inside the tree trunk. Just remember to watch some videos to get the speed right.
An alternative is a front porch hammock, which would make implementation a snap given all of the space in which to hide the mechanism.
A porch hammock also suggests a porch swing as another possibility...
And as an alternative to the porch swing is the glider, an easier thing to animate, and much more subtle.
Also see the rocking chair.