Chill canister of ice cream maker in the refrigerator while making the sherbet mixture.
Puree blackberries in blender or food processor until smooth, stopping to scrape down sides. Press blackberry puree through strainer to remove seeds (optional).
Add sugar, buttermilk, and vanilla to bowl and stir until blended. Pour blackberry mixture into canister of ice cream freezer and churn and freeze according to ice cream maker manufacturer’s instructions.