Preheat your oven to 350°F (175°C).
In a saucepan, combine sugar, cornstarch, and salt. Gradually stir in milk. Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil for 1 minute, then remove from heat.
Stir a small amount of hot mixture into beaten egg yolks, then return to hot mixture in saucepan. Cook for 2 more minutes, stirring constantly. Remove from heat and stir in coconut, butter, and vanilla. Pour into pre-baked pie crust.
For the meringue, beat egg whites with cream of tartar until soft peaks form. Gradually add sugar, beating until stiff peaks form. Spread meringue over hot filling, sealing edges to crust.
Bake in preheated oven for 10-12 minutes, or until meringue is golden brown. Cool on a wire rack.