Just impose a -1 internal penalty to each attack after the first with a firearm until the player takes a Reload action. The penalty represents “having less ammo”. Guns with large capacity magazines could have a Capacity trait that negates it. So if my AK with a banana clip has Capacity 3, I can take three attacks before I start having to be careful with my ammo.
Capacity, of course, would be relative to the gun. So a Capacity 3 handgun would have much less ammo than a Capacity 3 machine gun.
Then you can introduce an autofire mechanic which allows you to increase Dam by sacrificing higher penalty. “I get +3 damage by taking a -4 to my next roll unless I reload.”