I think that the community can largely agree that Cannons as an upgrade type are generally not seeing much play at the moment. They cost too much, do not do enough damage to justify not taking a standard attack, or in the case of the HLC requires a bullseye arc which you cannot rely upon getting. The question must be asked, what can be done about this?
One possible solution would be to reduce the points cost of the cannons, but this wouldn't solve the issue that in most circumstances pushing more damage (and potentially pushing criticals through) is preferable to taking a cannon shot. As I see it, there are two potential solutions to the problem; allow the cannon-carrier to double-tap, or otherwise increase the reliability of the cannon when used.
The first solution is perhaps the most straight-forwards. Such an upgrade couldn't be a Gunner, as most of the cannon-carrying ships do not have a Gunner slot, so I'd think that the Modification slot would be the best fit for such an upgrade:
Slaved Targeting
"After you perform a primary attack which hits, you may perform a bonus attack with an equipped cannon against the same target.
When performing a bonus cannon attack, the attacker cannot modify their attack dice."
Cost: Some Points (no more than 3)
This upgrade would reflect the ship having the cannons and 'normal' weapons being rigged to the same firing trigger, so when the pilot fires their primary weapon, the cannon fires as well. Also, if their primary weapon misses, the cannon fire would also be off target. They also cannot modify the cannon shot, as they aren't 'aiming' that weapon specifically.
An alternative to 'shoot more' is 'shoot better'; if I'm choosing to take an Ion Cannon, Tractor Beam or Jamming Beam, and am willing to sacrifice my 'normal' shot to fire them, I'd like to have a good chance of actually hitting with the bloody things! So, an alternative Modification upgrade would be as follows:
Redirected Power Couplings
"When you perform a cannon attack, you may gain a strain token to reroll a single dice.
If your primary attack value is '3' or above, you may gain a strain token to change a single dice to a hit instead"
Cost: No more than 2 points (I'd lean towards one).
The idea here is that when the cannon user attacks, they can shunt additional power from their other systems to have their cannon attack be more effective. It also gives ships which have higher attack values more incentive to use a cannon. It also uses strain, which is a mechanic which I really feel is underutilised at the moment, to give a trade-off which has to be considered.
(I love how this gif starts one way, but gets so extra by the end)