A quick fix would be "you remove the reload counter at the end of your turn" and always adding 2 counters when you fire.
I'm okay with this.
It would make it so you could either fire every other turn of yours, or overwatch every other turn. Both ways it is every other turn of use (assuming you can overwatch with it while it is recharging).
Using Madness' counter idea:
So, normal firing:
1A: Fire, add 2 counters. End of turn, remove one counter
1B: Charging
2A:Charging, remove one counter at end of turn. Can go into overwatch
2b: Charged, available to fire.
Overwatch fire would go like this:
1A: Go into overwatch
1B: Player A takes his shot, and adds 2 counters
2A: Charging, remove one counter at end of turn
2B: Charging
3A: Charging, remove one counter at end of turn. Can go into overwatch
3B: Charged, available to fire.
You could basically fire every other turn as normal, or every other opponents turn as overwatch. Both mean you skip a turn.