You can burn it, you can kill it's crew with arrows, but the only sure way to
Capture the Black Ship is to board it and win the boarding melee.
I managed to do that with 4 Mori Medium Bune and 4 Mori Bow Cowboya.
Tactics - Make the Black Sheep sail against the wind so it is slower and less maneuverable, engage from the front or rear of the ship, or at the worst case only from one side (never let it use both of it's powerful broadsides).
Let it make only one broadside with the cannons.
Send in your boarding ship and give it the order to board. as soon as the initial grappling is made and your boarding ship is starting to close in, use another ship to soak up the first broadside from the same side that your boarding ship is going to board.
A long distance for this "Heroic" role is preferable
Timing here is critical, your boarding ship
Must Not Receive The First Broadside!
After the boarding starts, move your ships around the fighting vessels, stay at close to medium distance and fire at will with arrows. Don't use fire arrows!
Use War Cries from your Bunes to demoralize the Black Sheep's crew, but only one at a time as their effect doesn't stack
As a safety, bring another potential boarding ship just behind the first boarding ship(facing the same way as well), this is in case your first boarder is not enough.
This has worked for me.
Happy hunting for Black Sheeps!
