Preheat oven to 175 degrees. Line 4 baking sheets with parchment. Trace nine 3 1/2-inch circles onto each sheet. Turn parchment marked-sides down.

Heat sugar, egg whites, and salt in a heatproof bowl set over (not in) a pan of simmering water, whisking constantly, until warm to the touch and sugar is dissolved, about 3 minutes. Remove bowl from heat. Whisk on medium-high speed until peaks are stiff and glossy, about 4 minutes. Beat in food coloring.

Dab meringue under corners of parchment to hold in place. Spread 3 heaping tablespoons meringue within edges of each traced circle. Sprinkle 1 teaspoon coconut each over 12 of rounds.

Bake until meringues are dry but not taking on any color and can be easily pulled off parchment, 1 1/2 to 2 hours. Let cool completely on sheets on wire racks.

Form 1/4-cup scoops of sorbet into 3-inch disks, using your hands or a small offset spatula. Place a sorbet disk on a plain meringue. Top with a second plain meringue and a second sorbet round, then end with a coconut-sprinkled round. Transfer to a parchment-lined baking sheet and freeze, at least 5 hours and up to 1 day. Repeat with remaining meringues and sorbet.