Nets and Cables
You would only get one to a few "shots", but large steel-wire nets would be effective against most pre-1930 aircraft.
The net is carried in a pod under the fuselage or wings; practical limit seems likely to be five pods for an aircraft small enough to be considered for attacking air-to-air.
When released, a sequenced set of catches let paddle-like "wings" on the trailing edge of the net pull it out of the pod and spread it, and additional "wings" on the leading edge, pulling the opposite direction, would keep it spread as it falls (the fall wouldn't be perfect, but doesn't really need to be). The tactic would be to fly close over the enemy and release a net from above and ahead, with the intent that the spreading net would foul the propeller or damage the fabric on flying surfaces, forcing the aircraft down (ofif not damaging it so much it broke up).
IMO, this would be the kind of thing only invented by folks who didn't have practical air-to-air gunnery. It would be more effective against airships, especially if also equipped with flares scattered over the net surface and hooks to punch through the airship's envelope and ballonets and allow igniting the hydrogen. The flares and hooks would give some increase in effectiveness against airplanes, as well, so likely would be on all or nearly all nets (there might be a tactical advantage for "clean" nets in some situations).
A possible variant of this would be a bolas-like contraption, a long wire with weights on the ends (or three wires connected at a center with three weights); this would tumble as it fell and be very difficult for the target to evade because it would be quite hard to see. If it strikes, it would wrap around wings or fuselage and constrict, possibly hard enough to tear through the frame inside the skin, or it would foul the propeller as a net would.