I knew I didn't want my airships to carry cannon; the idea of that much recoil in a lighter-than-air vessel strains credulity a bit. Machine guns would be a possibility, but rare, cumbersome, and not terribly effective against other airships. Maybe for a ground-assault airship, to 'sweep the deck' prior to debarking troops, but again, a very expensive, specialized device (Clockwork repeaters, or else primitive water-cooled weapons) not suitable for extensive dissemination.
What, then, could be used in airship-to-airship combat? Something recoilless, with the firepower needed to scuttle an enemy armored airship?
Rockets. Specifically, the Congreve and Hale models. The Congreve style will probably be launched from racks, and can't be reloaded in flight. They will lack accuracy, but are easier to load and use, and more can be fired faster. The Hale will be fired from interior tubes, venting fore and aft, similar to torpedoes. Thus, a Hale salvo is far more accurate, but requires a larger vessel, and can't fire as many torpedoes as a Congreve-equipped airship.