I mess about with CB's and multimode tranceivers as a bit of a hobby. I think CB's or Ham radios would be ok in a 156, just use the cigar lighter socket for power and a magnet mount on the roof for the antenna.
The last car I installed a rig (2m & 70cms) in was my LR Discovery almost 20 years ago. The roads round here are just too busy these days to safely operate mobile. I usually have one of these to listen to our local repeaters - fits nicely into the little storage compartment in the door, and very cheap for a dual band hand-held tranceiver.
I've got a mag-mount antenna but I think it makes the 156 look like a taxi...
Any more radio hams (licensed or otherwise) around?