Preheat oven to 350 degrees F (175 degrees C). Prepare a 12x9-inch baking dish with cooking spray.
Beat yams, eggs, 1 cup water, evaporated milk, 1 cup brown sugar, 1 cup white sugar, 1 cup butter, and vanilla extract together in a large bowl with an electric hand mixer until smooth; spread into prepared baking dish.
Mix flour, 1 cup butter, 1 cup brown sugar, 1 cup white sugar, 4 teaspoons water, and baking powder together in a separate bowl. Stir pecans and coconut into the flour mixture and sprinkle over the yam mixture.
Bake in preheated oven until the topping is lightly browned, about 45 minutes. Cool at room temperature 10 to 15 minutes before serving.