Combine the warm water, sugar and yeast in a glass bowl. Stir to dissolve, and cover to keep warm. Let it sit until bubbly, about 10 minutes. Add the coconut, and let it sit uncovered 5 more minutes.
Combine the flour and salt in a large bowl. Pour the yeast mixture and coconut milk into the bowl with the flour. Stir together with a wooden spoon until the dough starts to come together.
Turn the dough out onto a floured board and knead the softened butter into the dough. After incorporating the butter, continue to knead for 5 minutes on a wooden board. Add extra flour if necessary, but the dough does not generally stick, due to the fat content.
Form the dough into a ball and let it rest, covered with a damp kitchen cloth, in a warm place until doubled, about 1 1/2 hours.
Split the dough into two balls, and roll each of those into eight balls. Place each set of 8 balls in either a buttered 8-inch round cake pan (if you like them to stick together and be slightly softer) or on a buttered cookie sheet (if you prefer them to be separate and a bit crustier).
Preheat the oven to 350 F. Let the rolls rise another 30 minutes covered with a damp kitchen cloth in a warm place.
Bake for 25 minutes. Serve warm, as a snack or with a meal instead of a dinner roll.