Twister
Secure a tire at the end of the rope swing, and with a person seated with his or her legs through the center of the tire, "twist" the tire in a clockwise direction until the rope begins to tighten and you feel resistance. Let go of the tire and let the swinger "twist" as the rope untwists itself. For added fun, count the number of rotations each player makes and see who can reach the highest number.
Ball Toss
Thread twine or other cording through the handle of a small plastic sand pail and tie the pail around the waist of the first player. As the player swings back and forth on the rope swing, other players take turns tossing ping pong balls or small bean bags toward the swinger with the goal of getting as many objects as possible into the bucket. The swinger can wiggle during the swing to try and keep the ball or bag-throwing players from scoring points.
Jumper
If your rope swing is positioned toward a body of water of suitable depth, swingers can be challenged to try and catch a plastic ball thrown in their direction just as they release the rope and begin to plunge toward the water. Points can be given for the most spectacular catch, or for the most catches in a row. This is a good game to play in teams of two, with one member of the team tossing the ball and the other member of the team swinging and attempting to catch the ball.
Platform Jump
If you have ample room around your rope swing, you can construct a jump platform similar to that of a skateboard ramp, with a wider base at the top, or even use a simple but sturdy wooden box. Rope swing games that can be played using the platform include "highest swing" and "furthest jump."