I found this recipe this morning for you from Allrecipes to try. It has a sweet and tart flavor.
1 medium head red cabbage, cored and sliced
2 large tart apples, peeled and sliced
1 medium sweet onion, sliced and separated into rings
1 1/2 cups water
1 cup cider vinegar
1/2 cup sugar
1 tablespoon butter
1 teaspoon salt
6 whole peppercorns
2 whole allspice
2 whole cloves
1 bay leaf
2 teaspoons cornstarch
2 teaspoons cold water
In a Dutch oven, toss cabbage, apples and onion. Add water, vinegar, sugar, butter and salt. Place the peppercorns, allspice, cloves and bay leaf on a double thickness of cheesecloth; bring up corners of cloth and stir with kitchen string to form a bag. Add to Dutch oven. Bring to a boil. Reduce heat; cover and simmer for 1-1/4 hours.
Discard spice bag. In a small bowl, combine cornstarch and cold water until smooth; stir in cabbage mixture. Bring to a boil; cook and stir for 1-2 minutes or until thickened.