I hesitate to offer advice, since I can't shut Paddy up in the car but here goes with what others have previously posted and what I've read in training guides.......

Have you taught him to bark on command? Many people recommend this (I'm going to start this with Paddy again this weekend) - get your dog really excited (involves you acting like a hyperactive prat) and woof at him to get him barking. If you've got a clicker - click and treat. Otherwise - "good boy" all excitedly and treat. Keep doing this till he's reliably barking, then add the verbal command ("bark" or "sing" or whatever you want) and the non-verbal sign for "bark".
When you've reliably taught him to bark on command - then teach the "quiet" command - verbal and signal. It could be "shhh" - beyond the zone of the car, mine is (unimaginatively, but easy to remember) "Quiet"....
Anyway, that's the theory.
Now where's my muppet of a dog...ah yes, that will be him barking without having even been asked. Clever boy....

Denise