Pour butter into a 9-in. round baking pan; sprinkle with brown sugar. Drain peaches, reserving 6 tablespoons of syrup. Arrange peach halves, cut side down, in a single layer over the sugar. Sprinkle coconut around peaches; set aside.
In a large bowl, beat eggs until thick and lemon-colored; gradually beat in sugar. Add extract and reserved syrup. Combine flour, baking powder and salt; add to egg mixture and mix well.
Pour over peaches. Bake at 350° for 50-60 minutes or until a toothpick inserted in the center comes out clean. Cool for 10 minutes; invert cake onto a serving plate. Serve warm.