Preheat oven to 350 degrees F. Grease 9X13-inch baking dish.
In medium bowl, combine softened butter, sugar, and flour until combined and crumbly. Press into prepared pan.
Bake crust for 20 minutes, until crust is lightly browned. Remove from oven and cool slightly while you mix together the other ingredients.
In clean medium bowl, beat softened cream cheese until smooth then add in 1/4 cup sugar, eggs, and vanilla extract. Gently stir in drained pineapple. Spread over baked crust.
In small bowl, melt 2 tablespoons butter then toss in the shredded coconut to coat. Sprinkle buttered coconut over the pineapple cheesecake layer.
Cover pan with foil and cook 30 minutes. Remove foil then bake additional 15-20 minutes until coconut is browned.
Cool completely before cutting into squares.