
I have had this with a puppy - we began a process of desensitisation.
First of all we fed her in the back of the car, every meal, every day and left the back open. The car did not have the engine running. When she would get in without fear and would eat happily and sit in the back without wanting to get out, we then started the engine but still left the car stationary - all meals were fed here with the engine running, when she was completely happy with that we took her for a very short ride, all of 2 minutes, 4 times a day we did this and then gradually lengthened the time of the journey.
Some months later she would happily get into the car (always a treat in there for her) and eventually she would travel all over the country without sickness or diarrhoea - but by this time feeding of meals was done after the car journey.
It is the stress that causes the diarrhoea and the motion of a car upsets the balance of the inner ear and can cause the sickness. So he needs to associate the drive with something pleasant, somewhere nice at the end of the journey.