Hello, Bob, dioramas aren't my thing. For wargaming WW2, the issue is to be able to move the plane, so I put up with a stand that is not "invisible".
Scroll down to the Spitfire: I've scratchbuilt this type of thing using coathanger wire, painted green. Having a sturdy base that *won't* easily allow the plane to tip - disaster- is important. I use terrained hard wood.
Some people need their planes to dive or climb and use telescoping aerial. See:
These are very visible, of course.
Now your problem is different. Invisibility is the key. If your diorama has a roof, it would be easy to suspend the model using fishing line. Otherwise, a solution, not unlike mine (above) using clear perspex rods is about the only answer.