I can't find anything published in Baierisch or Boarisch, but in
this standard German text about the Bavarian 5th Infantry Regiment Preysing, at the very end circa 1803 there's a table examining pensions, and it breaks down the regiment by rank. The terms seem consistent with Prussian and Austrian terms of the era, they're definitely more outdated than what was used at the time of the book's publication, 1883, so I think it's reliable. It's a shame it's not in Bavarian German though. The most interesting quirk is that the two grades of captain clash, one is traditionally German and the other is borrowed from Latin (probably via French).
Oberst - Colonel
Oberstlieutenant - Lieutenant Colonel
Major - Major
Hauptmann - Captain (probably
Rittmeister in the cavalry, if Bavaria follows the pattern of other German states)
Stabskapitän - literally Staff-Captain, an administrative position when the Captain is present, a leadership position in his absence or refusal to lead (prob. Stabsrittmeister for cavalry)
Oberlieutenant - Upper-Lieutenant (First Lieutenant)
Unterlieutenant - Under-Lieutenant (Second Lieutenant)
Feldwebel - Sergeant Major
Fourier - from the French
fourrier, an NCO tasked with provisions and foraging. In the table it's equal with Feldwebel, but that may be only for pension.
Sergent - Sergeant.
Korporal - Corporal
Gefreiter - Private First Class, literally freed man, like a medieval servant-soldier rewarded for his service.
Gemeiner - Ranker, Private. In most German states this is replaced with something specific to the company's or battalion's class, like "Musketier", "Füsilier", "Grenadier", etc. Gemeiner is a convenient catch-all.