In a saucepan, whisk 2 cups milk and the 3/4 cup sugar. Bring to a simmer. Dissolve cornstarch into 1/4 cup milk. Whisk egg yolks together.
Temper egg yolks by adding a little of the simmered milk mixture to the yolks. Mix tempered yolks and cornstarch mixture into rest of simmered milk mixture. Continue cooking, stirring constantly, until thick.
Remove from heat and add butter, vanilla and coconut. Pour into pre-baked pie shell.
Make meringue by beating egg whites until firm. Gradually add in sugar. Spread meringue on pie and bake at 400 for 3-4 minutes until golden brown.