In a small saucepan over medium heat, cook the onion rings in the olive oil until they are translucent. Add the pineapple and sugar and stir until the sugar is dissolved. Add 1/4 cup of the pineapple juice and the balsamic vinegar and cook about five minutes, or until about half the liquid has evaporated. Add remaining pineapple juice and the cranberries and cook until the cranberries pop and the juice thickens, about five minutes. Stir in the thyme.
Can be made ahead and refrigerated for a week if tightly covered. Best if made the day before.
Makes 1-1/2 cups.