Combine egg whites (at room temperature), vinegar, cream of tartar, and salt in a large mixing bowl; beat until foamy. Gradually add sugar, 1 tablespoon at a time, beating until stiff peaks form. Tint meringue to desired pastel shade of green.
Spoon meringue by 1/2 cupfuls onto greased, unglazed brown paper. Use back of a spoon to shape meringue into 4-inch hearts. Shape each heart into a shell (sides should be about 1 inch high). Bake at 250° for 1 hour. Cool away from drafts. Spoon sherbet into heart shells and serve immediately.