Somewhat rare. Perhaps one could be obtained when sold out of the service, but I'm not too familiar with the fate of decommissioned vessels in the 1600s. Corvettes, however, were common among privateers, and were essentially lightly armed, fully rigged ships with frigate lines. They usually had an armament of ~22 guns, and were referred to as a "sloop of war." Basically, the frigate's smaller cousin.

Letters of marque or an equivalent can be given by a governor, so I'd say it's possible.