Begin by placing fresh pineapple rings in a large bowl. Pour dark rum and coconut rum over the pineapple until fully covered. Let the pineapple soak for at least 1 hour at room temperature, allowing the rums to infuse the fruit. Once soaked, drain the pineapple rings and gently pat them dry with paper towels to remove excess liquid.

While the pineapple is soaking, prepare your coating stations. Set up three separate bowls: one filled with all-purpose flour, another with a mixture of beaten large eggs and coconut milk, and the last with sweetened coconut flakes.

Take each drained pineapple ring and dredge it into the bowl of flour, ensuring a light coat on all sides. Dip the floured ring into the egg mixture, letting any excess drip off. Finally, press the ring into the bowl of coconut flakes to cover it entirely.

Heat vegetable oil in a skillet to 350°F (175°C). Fry the coated pineapple rings in small batches for about 1 minute on each side, or until golden brown. Transfer fried rings to a plate lined with paper towels to drain excess oil.

In a mixing bowl, combine softened cream cheese and powdered sugar, blending until smooth. Gradually stir in a few tablespoons of the reserved rum until reaching your desired consistency for the dipping sauce.