I don't think there are any, at least that I've seen. I'm not sure what you are looking for exactly either. I'm not really a simulationist kind of guy, so I'd probably consider the setting, the tier of play, what type of effect I was going for with it, whether the operators are assumed to know how to handle the cannon or if it's something done out of convenience, and what was needed in the story, and how big and advanced is this cannon?
It sounds like you're looking at the improvised actions and damage section of the DMG, so I'd say that puts you on the right track for making something appropriate up.
I'd probably make it something like 3 or 4 standard (or some number) actions to load and fire the cannon each time. Maybe allow up to 2 people to do it twice as fast (so it only takes 1 or 2 rounds, instead of 3 or 4) This could be made kind of dramatic if you have a horde advancing as you try to ready the cannon(s) and forcing them to choose between how they want to spend their time on what tasks.
If you are requiring 2 people to do it, I would probably break the rules on suggested damage and go higher, since afterall it's like improvised damage from TWO players, not just one! I'd probably have a primary target with the heaviest of damage, with splash damage around. I might adjust the damage based on whether the cannon can be fired again, or if it's a one time thing.