In a large bowl cream together the butter and 1 1/2 cups of sugar until light and fluffy. Beat in the eggs one at a time, mixing well after each one. Stir in the rum, pineapple juice and coconut essence until well blended. Combine the flour, baking powder and salt; stir into the batter. Stir in the pistachio nuts, pineapple and coconut until evenly distributed. Cover and refrigerate for about 10 minutes.
Preheat the oven to 180 degrees C. Lightly grease two baking trays.
Divide the dough into four equal parts. Form each piece of dough into a 30cm long log shape on a lightly floured surface. Place two logs onto each baking tray and pat down until they are about 8cm wide. There should be at least 5cm of space between each log.
Bake for 30 minutes in the preheated oven until firm but not crisp. Remove from the oven and allow to cool for at least 10 minutes.
Place the biscotti bars on a cutting board and use a serrated knife to cut into 2cm wide diagonal slices. Return the slices to the baking trays cut side down. Return to the oven. Bake for 8 minutes then turn the biscuits over and bake for an additional 8 minutes, or until lightly toasted. Cool completely then store in an airtight container.