Preheat oven to 325 degrees F (165 degrees C). Line a 9-inch pie plate with prepared pie pastry.

Beat sweet potatoes and egg yolks together in a bowl until smooth. Mix milk, 1/2 cup white sugar, coconut, melted butter, salt, nutmeg, and vanilla extract into sweet potato mixture; pour into prepared pie pastry.

Bake in the preheated oven until pie is set, 35 to 40 minutes.

Beat egg whites in a glass or metal bowl until foamy. Gradually add 6 tablespoons sugar, beating until meringue is glossy and stiff peaks form. Spread meringue over hot pie. Bake in the oven until meringue is golden brown, 12 to 15 minutes more.