The way it is done is to attach the feed at a point so many inches up from where the coax would be grounded to the fuselage. Although the fuselage is at ground potential where it connects to the battery and negative lead for the avionics if you find the right spot to attach the coax the feed will both be matched and radiation will occur on a vertical member as if it were insulated from ground.

Here is a web page showing how it is done for the lower medium to high frequency portions of the amateur radio band on a grounded tower, of course, with an aircraft you would have more trouble to find a sweet spot for loading into the frame than with a simple tower but I believe it can be done at the tail, if you feed the lower portion of the tail the remaining upper structure might be about the right length for VHF-AM in the aircraft comm band:

http://www.qsl.net/w9rb/webdoc9.htm

The drawing shown on this web page is for a ham radio tower with a beam antenna on top which has nothing to do with what they are trying to show. The drawing shows a parallel wire running up the tower and isn't exactly the method I am thinking of, the one I am talking about is where you ground the coax on the vertical member and then attached the center wire of the coax on the sweet spot where it loads properly, higher up on the tower.

If you are not an RF man with a through-line watt meter I wouldn't expect this to be an easy task for someone new to radio or antennas, but it could be done with a few hours work on a tube and rag aircraft if you did it before it was covered.

Only thing is the radiation pattern would doubtless be other than omni-directional and would probably favor the direction the aircraft is headed into much more than behind it, assuming the forward vertical tube of the tail is chosen to load into. This is very dependent upon the welded structure too, how much length of tube you have to work with, so many things would need to happen to be right that this method might be very difficult to achieve.

You could always use a vertical strip of copper foil to act as a radiator too, glued to the back side of the aircraft fabric as far away from support tubing in the frame as possible, it could be coupled with a matcher so that the length doesn't need to be a full quarter wave length and the frame of the aircraft could act as ground plane, one reason why you wouldn't want the copper strip to line up in parallel to any of the tubing.

All of this stuff would be a compromise, not a good antenna but one which would work in most situations but I wouldn't want to depend on it for communication if I were a long way from where I wanted to talk to.

The important thing about VHF-AM aircraft comms is that you keep the antenna vertical because if horizontal you loose a large amount of signal when communicating with a vertical antenna on the ground due to being at an opposite polarity if the aircraft antenna where horizontally oriented (transmit wave).

Although, for many situations it would work anyway, if you are close enough it won't matter, the signal scatters into different polarities all over the place as it hits other structures on the ground or the airframe itself anyway, but the majority of the power would be in the polarity the antenna is transmitting it at and should be the same as the polarity of the receivers antenna on the ground for maxiumum signal.

Unless you really need to reduce drag doing something like this isn't going to be the best setup, but people use hand held transceivers inside aircraft with nothing more than a rubber ducky antenna to talk to towers which is probably far more inefficient than a strip of copper glued to the fabric of the airplane to act as a vertical antenna, in that light it isn't too bad a way to go, as long as the pigment in the paint doesn't contain something metallic which would be a reflector to radio waves.

I am sure there are other ways of doing this which would work too. There are flat profile antennas which can be glued to the underside of the wing between ribs somehow. Also, perhaps loading into a landing gear leg would be much better than into the airframe tubing, since it is a single piece and hangs out below the aircraft.