Specific to the Black Prince, may want to look into some Irish historical information.
Going through a sampling of the Ben Franklin papers led to a whole web (no pun intended) of tantalizing possibilities. It appears that the story relayed at this link captures the meat of the ships history:
Here are a few excerpts:
"Luke Ryan and Edward Wilde of Loughshinny had become partners in a large smuggling vessel, the Friendship with fourteen swivel guns and a crew of sixty Rush men. In February 1778 the Friendship was fitted out at Sir John Rogerston’s Quay and converted from smuggler to privateer."
"The Friendship sailed from Dublin in February 1779 and returned by the end of May. It now appears that the Friendship was bought by the Dunkirk armateur Jean Torris, and both Ryan and Wilde (sometimes known as McCatter) were minority owners. Torris was in the unusual position of owning a privateer that still carried an English admiralty letter of marque.
The Friendship had returned to Ireland with contraband goods probably bought from Torris. The Irish revenue defined both Ryan and his first cousin Wilde of Rush as piratical smugglers. John Draper, Superintendent of Excise for Dublin Port, arrested the Friendship at Rogerstown with Wilde and some crew members and impounded the goods. Later, Wilde and some other members of the Friendship crew broke out of Black Dog Prison at Ringsend and boarded armed wherries which had arrived from Skerries. They took the Friendship, the revenue guard cut the anchor line, and they sailed back to Rush. Here, they collected Ryan and more men and sailed south-easterly to Dunkirk after leaving the revenue men on shore in Dorset."
"On arrival in Dunkirk, Jean Torris renamed the Friendship the Black Prince with Ryan in command and Edward Wilde (alias McCatter) and Patrick Dowling as his officers. Later Benjamin Franklin through Torris had commissioned the Black Prince as an American privateer with an American letter of marque. The only stipulation was that an American merchant seaman Stephen Marchant from Boston would be listed as captain to fulfil the legal requirements."
So - may be able to track back a bit further into the Friendship.
Note that there are conflicting descriptions in various sources - some describe her as a Sloop, others as a Corvette, and still others as a Cutter.