It's more developmentally appropriate to play games that focus on developing those skills, rather then playing a sport. At that age, they really don't have much for competitiveness in them or follow the rules, even.
For example - instead of playing soccer, have a few activities that focus on kicking, dribbling, and stopping the ball. Instead of playing baseball have activities that focus on throwing and catching.
One activity I've seen related with throwing and catching is to have two teams, one on each side of the gym/playing area. Set up different targets - a hula hoop on the far end of the gym is worth 10 points, a bucket near the center line is worth 2 points, etc. Then have the teams throw soft balls or beanbags across the line. Blocking throws is allowed.
You can find plenty of fun activities on PE centered websites. I posted one below for ideas...