Jeffrey Steingarten includes a recipe for Black Mulberry Granita in his book "The Man Who Ate Everything".
I'll reproduce it here, but if you don't have the book, you should go grab it.
1/2 lb black mulberries or wild strawberries
2 cups spring water
1/2 cup superfine granulated sugar
juice of 1/2 lemon
puree the mulberries or strawberries in a food processor and ensure you have 2/3 cup of puree. scrape the bowl well and mix with the other ingredients. pass it through a strainer coarse enough to let through just a few seeds and bits of pulp. cover, chill, and freeze.
he also enjoys preparing it with 3 cups of water instead of 2, which he finds more refreshing but not nearly as intense.
his method for freezing/making the granitas:
pour the mixture into one or more shallow metal trays and place them in a freezer.
after a half hour or an hour, when ice crystals begin to form, stir them into the liquid.
repeat a half hour later.
freeze overnight.
remove, leave at room temperature for five minutes or so, and scrape the surface with the tines of a fork. spoon the shaved crystals into chilled serving dishes.