In a medium saucepan, combine sugar, flour and salt over a medium heat; gradually stir in milk. Cook and stir over medium heat until the mixture is thick and bubbly. Reduce heat to low and cook 2 minutes more. Remove the pan from heat.

Place a strainer over a clean mixing bowl; set aside.

Beat the egg yolks slightly. Gradually pour 1 cup of the hot custard mixture into yolks, whisking constantly. Return the egg mixture to the saucepan and bring the entire mixture to a gentle boil. Cook and stir 2 minutes before removing the pan from heat. Immediately pour custard through the strainer.

Stir butter, vanilla, and coconut into the hot mixture. Pour the hot filling into the baked pie crust. Cool and refrigerate until set, about 4 hours.