If the battery holds a charge and starts fine, then alternatorsounds likely. I just had the same thing going on in a Plymoth Caravan and had to replace the 10 month old battery--free under warranty. Upon checking alternator /voltage regulator functions were fine--good voltage output.

One thing I would say is pretty likely and that is that the car is getting insufficient voltage. Other than that, testing seems in order if the battery seems to hold a charge over night. Wont be able to verify if it spends the night on the charger.