Airborne units really should not be a tech. The first parachute jump from an airplane happened in California in 1911, well before the start of WWII. The good news is it is not that hard to incorporate airborne units and rules into just about any version of Axis and Allies.
My airborne units and transport planes are from Historical Board Gaming. I painted them to look like this:
Allied planes have invasion stripes on the wings to identify them. Axis planes have a white tail stripe. Here are the rules we use with them:
AIRBORNE INFANTRY:
Cost: 4
Attack: 1 (2 during air drops)
Defense: 2
Move: 1
• Airborne units are infantry that are specially trained to drop from Transport planes by parachute into enemy territory.
• Airborne units attack at 2 during any battle when dropped by parachute, to represent the element of surprise. In any other game situation they fight like regular infantry.
• Airborne units cost more than regular infantry due to their specialized training.
• Airborne units cannot retreat from an airborne assault.
TRANSPORT PLANES:
Cost: 4
Attack: 0
Defense: 0
Move: 4
• Transport planes (TPs) are used to carry 1 regular infantry or 1 Airborne infantry per plane.
• TPs cannot be used in an attack other than delivering Airborne units. They must first survive fire from any enemy AA guns in the territory attacked, then they drop their units and leave the battle. If a transport plane is hit by AA fire, both the plane and the airborne unit are lost with no chance to fire.
• Your TPs can only land in territories under friendly control since the beginning of your turn. (Time must be allowed for airbases to be set up.)
• Each TP can fly and carry one infantry unit per turn up to four zones.
• TPs cannot land on carriers.
• TPs have no attack or defense value. They can be taken as casualties when defending. They cannot be used in any attack other than by dropping off airborne units and withdrawing.