There is a historical/geographic phenomena known as a "pirate coast" in which the area just behind the coast is so mountainous or inhospitable that there is virtually no easy communication with the interior. That means that an interior government has no control over the coastal communities and they get no support from the interior, so they invariably turn to piracy. Two of the earliest examples were the Aegean coast of Anatolia and the Dalmatian coast of the Adriatic: mountainous interior, no strong government influence = Pirates!
Which means that a possible "pirate Civ' mechanic could build on the current 'coastal barbarian clans': when one of them becomes a City State, it becomes a Pirate City State like, say, Port Royale, Tortuga, Hai Tac, Sale, Porto Farina, Algiers, etc.
Any of these could also be the basis for a "Pirate Civ" in which your starting bias would be 100% Coastal Start, you would have bonuses towards sea trade and commerce but severe maluses towards building land armies, Pirate type ships as posted earlier might even be free or dirt cheap since your population will be building them and using them without 'government' supervision: something like every time a ship pillages a coastal tile or loots a Trade Route it spawns a new 'pirate' ship - success breeds imitators, so to speak. . .