Sorry, this isn't possible. Weapons are one of the things that are hardcoded into the game, and not in any of the .txt files. The closest thing you could do would be to add twice the phasers (if you wanted them to fire twice as fast) and choose to fire the original amount, and then fire the remaining phasers half a turn later. Would take twice the energy to fully charge, though.
But phasers are already the fastest-charging weapons, other than a certain drone rack, so they're pretty darned good already...