Preheat oven to 400 degrees F (200 degrees C). Grease a 9×9-inch baking dish.
In a large bowl, combine flour, brown sugar, white sugar, baking powder, salt, and vanilla. Pour milk into dry ingredients, and then stir in melted margarine. Mix thoroughly.
Pour mixture into prepared baking pan. Arrange peaches on top and sprinkle with cinnamon. Bake in preheated oven until golden brown, about 30 minutes.
To use fresh peaches, you may substitute 4 cups peeled, sliced peaches for the canned peaches. To peel peaches, bring a pot of water to a boil. Remove from heat. Carefully drop peaches into hot water; let stand for 1 minute. Use a slotted spoon to transfer peaches to an ice water bath; when peaches are cool enough to handle, skin will slip right off.
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