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Preheat the oven to 170 °C.
Beat the eggs with the brown sugar. Add the melted butter, then the yogurt. Stir in the flour, baking powder, salt, and shredded coconut, just enough to form a smooth batter.
Pour half of the batter into a buttered or lined loaf pan. Spoon the fig jam into the batter in small dollops, then cover with the remaining batter. Run the blade of a knife through the batter once or twice to create a marbled effect.
Bake for 40 to 45 minutes. Check for doneness with the tip of a knife, avoiding the areas with jam. Let cool slightly before removing from the pan.
