Preheat the oven to 350 degrees F (175 degrees C). Spray a 10-inch fluted tube pan (such as Bundt(R)) with cooking spray.
Beat cream cheese and butter together together in a bowl using an electric mixer until creamy. Add white sugar and mix until light and fluffy. Add eggs and flour in an alternating fashion, starting and ending with an egg and beating well after each addition. Add almond extract, pineapple extract, and food coloring; mix batter well.
Pour brown sugar evenly into the bottom of the prepared pan. Arrange pineapple rings on top of sugar and place a cherry in the center of each. Pour batter evenly over pineapple.
Bake in the preheated oven until top is golden brown and springs back when touched lightly, about 45 minutes.