Cut pineapple into 1/2-1" rings, and place into baking dish.
Mix together brown sugar and rum and pour over pineapple. Turn pineapple over to coat. Let marinate for 5-30 minutes.Toast coconut by placing in a small (dry) fry pan, over medium-high heat. Shake pan often and remove from heat once starts to turn brown, about 7 minutes.
Place pineapple rings on hot grill (spray with a bit of oil if you like), and grill for about 3 minutes per side. Use the marinade to baste the pineapple as it cooks (caramelizes).
To serve, place 2 rings on each plate, top with a scoop of ice cream, drizzle on some of the rum marinade if you like, then sprinkle on the toasted coconut.