Preheat oven to 350°F (175°C).
In a saucepan, combine sugar, cornstarch, and salt. Gradually whisk in milk and coconut milk until smooth.
Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil for 1 minute, then remove from heat.
In a small bowl, beat egg yolks. Gradually whisk in 1 cup of the hot milk mixture. Return to saucepan, whisking constantly. Cook for 2 minutes, then remove from heat.
Stir in butter, vanilla, and shredded coconut. Pour filling into pre-baked pie crust.
In a large bowl, beat egg whites and 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 for 12-15 minutes, or until meringue is golden brown. Cool completely before serving.