I've been googling around for a half hour, and I cannot find anything about gentian violet staining the stool. I did find a Q&A on the LLL site about a mama whose baby had black stools after using gentian violet, and the conclusion was that her nipples had been bleeding, and it was the blood staining the stool black. If your nipples are cracked or raw, that might be an explanation.
I do know that iron supplements can cause black stools. Has baby recently started any supplements, or started iron-fortified cereal?
I think I'd be mildly concerned, if none of this rings a bell for you. Black stool can sometimes mean blood in the stool, which would be worrying if you can't find any simple reason for it-- I would wonder if baby was having an adverse reaction to the GV, for example, or if maybe there's something unrelated going on, and it's a coincidence that it started just now. I think I might mention it to a health care provider, if it keeps up, or if you can't find an explanation.
I just noticed you said brownish-- I think that would worry me less than very dark or tarry black.