Drain fruit cocktail, reserving 2 tablespoons of the syrup. Place fruit cocktail in a medium bowl. Set fruit and syrup aside.
Peel orange and cut into bite-size pieces. Add to fruit cocktail. Stir in 1/2 cup coconut until blended. Chill until ready to serve.
In a small bowl, mix mayonnaise and 2 tablespoons reserved syrup until blended. Set mayonnaise mixture aside until ready to serve.
To serve, place salad greens in a salad bowl. Add well-drained fruit mixture and mayonnaise mixture; toss lightly until all ingredients are lightly coated.
Garnish with additional coconut.
Serve with roast beef sandwiches, hot dogs or spaghetti with meatballs.