Is it possible to make a capital ship produce frigates?

As a frigate factory, no.  That said, the Rankulas spawns frigates, as do the Sova and Vulkoras.  In addition, you could always stick something like Returning Armada on a capital.

You can take the Sova's ability as an example and have it spawn any frigate you like.  In fact, just change the frigate type in the Sova ability and boot it up as a mod and watch a different frigate come out.  Nothing to it.