Black Betha is a galley captained by Ser Davos Seaworth. His son, Matthos, is one of the crew. The ship is probably named after Betha Blackwood, the queen consort of King Aegon V Targaryen who was known as Black Betha.
A Clash of Kings
Ser Davos Seaworth sails Black Betha north from Gulltown to White Harbor to distribute Stannis Baratheon's claim against the legitimacy of Cersei Lannister's children with King Robert I Baratheon. It returns to the fleet while it is blockading Storm's End.
Black Betha is part of Stannis's fleet that sails into Blackwater Bay during the Battle of the Blackwater. It rams and sinks Lady's Shame with the aid of Lady Marya, which is commanded by Davos's son Allard. Black Betha successfully boards White Hart. After Swordfish rams the hulk filled with wildfire, Black Betha is engulfed by flame and destroyed.