Chevrolet: 1992 Lumina problem, altanator, start ups

Question
I have a problem with a 1992 Lumina involving batteries.  Last month I replaced the battery after it had failed.  Earlier this week the new battery also failed.  The battery discharged when the car had sat a couple days between start-ups.
No lights had been left on, no doors left ajar, etc. The charging system is working; the alternator is ok.  I'm wondering what the problem might be.  What would be the best way to go about troubleshooting the problem?  Thanks.

Answer
OK let me see- if you have put in new good batterys and they keep going dead, I would first put a gauge on it and see what you get when running than shut it off and see what you have if it is low you have a dead short,  did you check to see what you are getting to the batt as charging voltage ? also what is the altanator putting out ? and is your belt loose? as that could do it all. so if all is ok I think you have a dead short  or a bad altanator  or  some wire is grounding out  and it is causing you to loose the charge over night or over a few hours, you will have to get a multi meter to test each thing by itself till you find where the short is  so good luck and let me know what you find or if you need more help let me know
bigw45/roger