you would need an old technology from the 1960s... and modify it to a machine gun rather than small magazine.
The Gyrojet. A totally recoil-less gun and the "bullets" ( small rockets ) stabilize themselves in flight. Not that accurate at long distance and not that dangerous at close range... but deadly at 30 meters or more.
https://en.wikipedia.org/wiki/Gyrojet
Of course they would need to redesign the entire gun and ammo but it would give them a real advantage when mounted on a light weight drone. Fortunately I believe the barrel of the gun would be easy to machine as tolerances are not that fine. A machine gun adaptation (which the makers planned but never implemented) should be possible too, but only at a modest firing rate given how the guns operate (no explosive charge).
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