Place cranberries, applesauce, and apple juice in a medium sauce pan over medium-high heat and bring to a boil.
Reduce heat to medium and simmer for 30 minutes, stirring occasionally, while allowing much of the liquid to be reduced down.
Taste to check for desired sweetness, and add sweetener if needed. Remove from heat and cool completely.
Transfer to a covered storage container and refrigerate at least 4 hours before serving. Transfer to a serving dish and serve.
Make ahead tip: This is a perfect make ahead recipe! It needs to be refrigerated 4 hours before serving, but you can make it up to 48 hours in advance. No re-heating is necessary, just transfer straight to a serving dish and enjoy.