MT, the differential wouldn't matter as long as it's big enough. The swap would be a lot of work but very doable, just need the parts. A lot more expensive than on a jeep or a truck though.
The question would be if Chrysler already makes different rear ends for the charger. If they do, then he could just swap it out, especially if it's the deeper gear that he wants. But I don't think many people do this since I've never heard of it done.