You could:
-have 2 cameramen sit in the back seat and film profiles from the back for the main angles using car mirrors and exteriors for cut-aways... as kind of a more "gritty indie" choice..
-rent camera mount(s).. the professional but expensive option
-lie down on the hood of the car with one camera per outstretched hand... the crazy stunt-man don't-try-this-at-home method...
-film from one side in another vehicle with a two shot of both actors in frame using tighter cutaways to switch between takes and scrap the shot-countershot thing... filming from another vehicle is hard though and will cause many many takes...
-use a greenscreen and film the thing in your garage while stationary... might be more effective but unless you get the chroma right it could come off looking fake
-shoot each scene twice for each actor's take... hardest on the actors but would definitely get you results... we did this once, where the actor not being shot would read from the backseat... though I tell you, it's not easy to be a camera-man and driver at the same time...
I think the easiest low-budget solution in this case would be to simply change the angles so you can shoot it with what you have... if it's one camera, maybe do a panning shot from the back seat for your master and then individual takes for each actor from the front with some cut-aways to give you coverage to edit with... if you have two cams, maybe try getting the shots from the backseats, or get creative with some mirrors from your house... or have all the dialogue happen at a red light or stop sign... or maybe turn all the dialogue into a voice-over and just use exteriors of the moving car... there's lots of options- just figure out what you have versus what you want and then shoot it the best you possibly can... and if you can't, either re-write, re-plan or re-do.
That's the best i can come up with, hope it helps!