Welcome from CA. You may already know this but there's still some unexploded ordinance along the central coast. So be careful what you dig up. There's also old pipelines from offshore wells that have been capped. I've also heard stories about the military setting up tank & anti-aircraft decoys (just pipes under camo netting) during WW2 to make any potential Japanese spy planes think the central coast was better defended than it was. A lot of that stuff was just abandoned after the war.
Can't say I'm as familiar with the SB coastline as Morro Bay. But that part of the Central Coast has a few other possibilities besides canons.
If you did find a canon, I'd think it would be exceedingly rare. Without good roads, moving canons around was extremely difficult. During the transition from Spain to Mexico, there were some big Indian rebellions & the Mexican army had a hard time keeping control of the inland areas. It took a while before they could get a canon out to (what is now) Modesto to deal with Estanislao's rebellion & blow the palisades. If one sunk off a shipwreck, I'd guess it would be found pretty close to where it fell since they don't float a bit.
