In a small skillet set over medium-high heat, stir together the apple juice, brown sugar and butter. When the sugar has dissolved and the butter has melted, add the onion and pinch of salt.
Lower the heat to medium and cook until the onions start to soften and clarify. Add the cranberries and cook for 2-3 minutes. Add the pomegranate arils and cook another couple minutes. Stir in the red wine vinegar, and when the skillet looks to be almost liquid-free, remove from heat and transfer the relish to a small bowl to cool. Enjoy or refrigerate for later use.