Sounds like the voltage regulator in the alternator may be bad.
The alternator should be changed in this case.
Overcharging the battery can harm it and that may need to be replaced if the acid leaked out.
Good luck on this repair.
Maybe try a salvage yard for the part.
NOTE: Under and overcharging are typically caused by a defective alternator, or its related parts (regulator). The voltage regulator is internal to the alternator assembly in many vehicles. Faulty wiring and other problems can also cause the charging system to malfunction. Further testing, which is not covered by this book, will reveal the exact component failure. Many automotive parts stores have alternator bench testers available for use by customers. An alternator bench test is the most definitive way to determine the condition of your alternator
Removal and Installation
To Remove:
NOTE: The OEM Denso SC1 (KG9) alternator is serviced as a complete unit only.Before servicing the vehicle, refer to the Cautions and Warnings in the beginning of this section.
Remove or disconnect the following:
Negative battery cable
Drive belt
Engine cooling fans
Wiring harness at alternator 
Wiring harness connector
Reposition the protective boot from the alternator output BAT terminal (for access).
Alternator output BAT terminal nut
Positive lead
Alternator mounting 
Loosen the lower alternator bolt (C).
Alternator bolts (A,B) from the alternator
Alternator from the vehicle
To Install: Position the alternator to the A/C compressor and engine.
Install or connect the following:
Alternator mounting bolts
Torque to 37 ft. lbs. (50 Nm)
Wiring harness connector to the alternator
Battery positive lead
Alternator output BAT terminal nut
Torque to 111 inch. lbs. (12.5 Nm)
Press the protective boot on the alternator output BAT terminal
Engine cooling fans
Drive belt
Negative battery cable
Test drive the vehicle.
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I will try changing this. ($1000) but I have heard that this does not fix the problem.I hope it does.
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