For Blackberry cider what I do is make a base cider with as many different kinds of apples as I can get, but about 60% sweet, like yellow delicious, about 10% Granny smith, 30% Ida Red, NorthernSpy, and whatever else I can find.
When its done I age if for a few months to clear. I get frozen blackberries from the grocery store and put them in a 1 gallon jug and add the cider I keep it cold and the fermentation won't kick off again. Its ready in a week or so,but needs to be consumed fast so it doesn't re-ferment. There's lots of other ways but this is the easy way to get real blackberry flavor.