RINSE THE APRICOTS, slit the sides and remove the pits with a small spoon, leaving the apricots intact. Replace each pit with an almond. Place the apricots in a bowl and sprinkle the slit sides with the rum. For the batter, combine the dry ingredients in a bowl and whisk in the water, then the melted butter. Pour the oil into a 4-quart pan and heat it to 350F. With a fork, dip the apricots into the batter and add to the hot oil 3 or 4 at a time, frying them about 6 or 7 minutes, until the batter is a deep golden and the apricots are cooked, but still firm. Drain the fritters on absorbent paper as they are fried and keep them warm in a 300F oven. To serve, sprinkle the fritters generously with confectioners' sugar.