Heat oven to 375 degrees F. Place butter in 9 x 9 x 2-inch-square baking pan. Place in oven to melt.
Remove the pan from the oven. Stir in the maple syrup, brown sugar, lime juice and allspice. Halve the bananas crosswise, and then halve lengthwise. Arrange the bananas, cut side up, in the pan. Sprinkle with the coconut.
Bake in the 375 degree F oven for 12 minutes, turning the bananas over halfway through the cooking and basting with liquid in pan.
Place the bananas in 4 dessert bowls. Top with vanilla yogurt. Spoon the sauce from the baking pan over the bananas and yogurt.