Hmm well i have not made it myself but i have a bunch of blackberries in the freezer for that purpose - if not then blackberry white sugar wine.
I, personally, would be inclined to try and juice the blackberries in the fruit press i use for cider, add some water to reduce acidity, and then add about 2 or 3 lbs of honey to it to make a gallon.
Another option would be to get matching weights of blackberries and honey, crush the blackberries, put them in a big pulp bag stretched over a bucket rim, and pour on a certain volume of hot water to get the juices out then melt the honey into that water. Might be worth macerating the crushed berries, contained in the pulp bag, in the manner that you might macerate grape skins in a red wine.
I'd add nutrients, too, because even with the blackberries the honey probably doesn't have enough nutrients in it for a decent fermentation.