Aeroplanes are fitted with hooks, rather akin to arrestor hooks in function, both above and below their fuselage. Wingtip hooks can be added if very large rudders are fitted, although this might be classed as a hand-ball. The hooks would look more like a pitot tube or refueling probe than a 'hook' shaped
thing, but would be hinged at the elbow with a pneumatic ram.
A balloon is filled to be approximately neutrally buoyant at a certain altitude, say, 10000ft. It should be spherical and without anything projecting from it except for six loops of such a diameter that they can be picked up by the hooks of passing aircraft.
The hooks are oparated by a pneumatic ram on each to launch the ball, 'kicking' it. It can also be used to drop the ball by opening the hook slowly. The rams are fitted with bypass excess-pressure valves to allow the ball to be ripped from its grasp by a tackling aircraft grabbing a different loop on the ball.
This might all actually be better done with electromagents.
The goalkeeper is a helicopter, with its blades gaurded by a large ring around the rotor tips. The goals would be large rectangular airships. All participating craft are fitted with ejector seats.
Rules are similar to the ground-based game. This might have to be named Aerial Soccer before someone across the pond has a nasty accident.