Preheat the oven to 180°C (356°F) and line a loaf pan with parchment paper.
In a large bowl, whisk together the melted butter, Greek yogurt, and sugar until smooth. Add the eggs one at a time, whisking gently after each addition until fully combined.
Sift in the flour, baking powder, and salt (if using). Stir until just incorporated—do not overmix.
Fold in the lime zest, lime juice, and shredded coconut, ensuring the batter is evenly mixed.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 50–60 minutes 180°C/355°F, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool completely before frosting.
Once fully cooled, spread the frosting made by mixing the cream cheese with powdered sugar.
In a bowl, beat the softened cream cheese with powdered sugar until smooth and creamy. Spread over the cooled cake and sprinkle with grated lime zest for a fresh finish.