To make the syrup: In a medium saucepan, add the water, sugar, fresh blackberries and lemon juice. Place the pan over medium heat and stir the mixture until the sugar dissolves and the berries begin to break down. Bring the mixture to a gentle boil, then lower the heat to a simmer. Let it cook for about 10 minutes, stirring occasionally. Remove the pan from heat and strain the syrup through a fine sieve to remove seeds and pulp. Allow the syrup to cool completely. It should make 1.5 to 2 cups of syrup.
In a large punch bowl, pour the cooled blackberry syrup.
Add the dark rum (or vodka), black cherry juice, and pomegranate juice.
Stir well to combine. Just before serving, add plenty of ice and gently top off with club soda to maintain the fizz if needed. Optionally, garnish with a few fresh blackberries.