Motor is a great alternative. Actually is used OTL in some cases. Engine works too, probably initially being called "road engines" to distinguish from "tank engines".
Motorcoach/motorwagon as an alternative to 'automobile' would be interesting.
Like others have said, wagon is already used in other languages for cars.
Another idea: the Ford
*Edit* saw Lemonflavored had the same idea!
I see you ignored where I posited it first