I checked my sources and could not find a recipe specifically for blackberry butter. But there's no reason it wouldn't work. Butters different from jams only in their lower amounts of sugar (about half as much).
Personally, I'd be concerned about the seeds in blackberries. But if that doesn't concern you,
I imagine you can use blackberries the same as grapes. Basically that means removing any stems, crushing the berries, and cooking in their own juice.
Add 1/2 cup sugar to each cup of pulp and cook down, stirring often to prevent sticking and scorching. When it's thick enough to round on a spoon, put it up same as your apple butter---processing in a bwb for 10 minutes at sea level.