My hillbilly way helps diagnose a little bit.
Turn it on, and literally turn on anything electrical you can. Wipers on full tilt, rear defrost, hazards, brights, a/c, blower on high, fog lights, etc. Then check your amps and volts, they shouldn't falter much if it is a good alternator.
In my opinion if you are going through batteries that fast you've got something going on unless you do a LOAD of starting/driving. Take the alternator off and have it bench tested at a parts store and go from there, but if it was me I would replace the alternator anyways if you have some doubts about its capabilities. I'm sure a professional will disagree but I'd replace both and hopefully the battery is still under warranty.