There's always the expensive solution to 'persuade' them to go away. http://upload.wikimedia.org/wikipedia/commons/e/ea/BB61_USS_Iowa_BB61_broadside_USN.jpg
You'd be more likely to hit the protected ship than the dinghys with that
PT boat sort of small attack ships equipped with big fuel tanks and armed with small caliber automatic cannons and an armed crew could probably do more. It would require couple of "PT" boat tenders and a bunch of the "PT" boats, but that's less of a problem than trying to find and operate 10 frigates in the area.
Bogues with choppers instead could be handy too, but there isn't any and the next available choice is too few and expensive. Choppers too would be expensive to operate. Though bogues with those brazillian turboprop fighters could be neat (yeah yeah, I know, they're not designed to operate from a carrier. make it happen!). Far less expensive to operate than choppers and travel faster. Although it may be better to design a whole new plane which is purpose built to fight pirate vessels. It wouldn't need much and it'd be cheaper. A single engine cessna with more powerful engine, strenghtened landing gear, a hook, some armour against small arms, guns and capability to operate at night (not just fly, but combat the pirate vessels) would do.
