I experimented with privateers in several games and found:
Privateers (ADM=2/1/4) lose to galleys (1/1) about 1/3rd of the time when attacking.
Privateers lose to coracles (1/2) about 60% of the time.
Even when privateers do not lose they rarely survive an attack with full hit points intact and must return to a port to heal.
If you have a tech advantage so that the enemies have only galleys available for a period of time then you may be able to exploit the privateers somewhat but in general they are not cost effective because of their low advantage.
If they had a low bombard strength with a high rate of fire that would get them closer to being of value. Also naval units that can freely move in and out of the ocean and sea should be able to retreat from combat into their advantage zones. It is not logical that a cannon weilding and ocean pirate ship would fight it out to the death with a fragile arrow pitching galley that can only hug the coasts. The pirates would swoop in and either sink the galley or just do as much damage as possible and then retreat back into the blackness of the open ocean and use their superior speed to survive and return at another location. (The naval retreat ability should be controlled by a special unit ability flag called "retreat to open water".)
Privateers should have a transport capacity of 2 to let them carry raiding parties of foot units only (just like pirate ships really did).
Privateers should also get a gold bonus for every ship that they sink (read this as attack, board, loot, rape, pillage, then scuttle). This is what pirates did you dummy!!! They attacked ships to steal the cargo and get rich. This would be somewhat like the barbarian village bonuses of 25 or 50 gold per village. Capturing an enemy vessel with a settler or workers on board should yield slaves that show up in the nearest friendly city or town or back in your capital. (Naval victory bonus abilities should be controlled by two special unit ability flags called "Bounty from Naval Victory" and "Capture naval slaves")
Another option would be to pirate strategic and luxury resources (just like really happened in the Carribean and in the Indian oceans.) If the pirate ship has the "steal resources" flag checked, then there would be a probability of gaining the use of a luxury resource for 10 or 20 turns when an enemy vessel is sunk. This probability should be controlled in the editor and the resources should only be available when the captured ship comes from a civ that has the resource.