I have been in search of dairy and mayo free coleslaw that I could make from scratch and I finally found this one in "The Smitten Kitchen Cookbook". The results are marvelous. If stored in an airtight container, it will last up to one week.
1 medium head green cabbage cored and thinly sliced or shredded (about 2 1-pound bags of coleslaw)
1 large seedless or English cucumber (about 1 pound), sliced in round discs as thinly as possible
2 tablespoons chopped fresh dill
½ cup (120 ml) white wine vinegar
1 tablespoon kosher salt
4 teaspoons sugar or one packet of Splenda
½ cup (120 ml) cold water
Toss the cabbage, cucumber, and dill together in a large bowl. Whisk the vinegar, salt and sugar together in a small bowl until the salt and sugar dissolve. Stir in the water. Pour the liquid over the salad, and let it marinate, tossing the cabbage occasionally. After 1 hour, it should be a bit wilted and crunchy; at 2 hours, the flavor is even better.