"Standard sized" 9VDC Alkaline batteries (a battery of six AAAA cells typically) is rated for ~500mAh nominally from what I've been able to determine. 9VDC Lithium are probably in the ~800mAh range.

Rechargeables are in the ~120mAh to 250mAh range, unless you go to a larger form-factor.

The big problem is that as you crest over C/20 (sustained load at 1/20th of rated capacity) and head towards C/10 depletion rates, things like internal resistance and resulting voltage-drop / heat become painful.