Take the battery to Checker, Kragen, Autozone, whatever. Have it tested on the charger, not the hand-held tester. If it takes a full charge and shows as good, remove alternator and take to the same and have them do a bench (charging) test on it, not in the car!.... If it fails, you know what to do...If it passes, check your ground first. Then, check all cables for corrosion. If all is good, replace or check ballast resistor, then the voltage regulator. If you're still having problems, check your wiring. (Ebay sells wiring diagrams for cheap)

Hope this helps...Been there.