Cut 2 rounds from each slice of bread, using a 2-inch biscuit cutter. Reserve excess bread for another use. Place rounds on a baking sheet; broil 5 1/2 inches from heat (with electric oven door partially opened) 1 to 2 minutes on one side or until golden. Let cool.
Combine cream cheese and green onions. Spread cheese mixture evenly on untoasted sides of bread rounds. Top each with 1 teaspoon radish, lightly pressing into cheese mixture.