If you're able to create ammunition--that is, if you aren't limited to what ammunition you found for it--then I'd say you should be able to prepare specially-made "poisoned bullets." They just wouldn't be poisoned in the same way as an arrow would. Usually, a poisoned arrow is dipped in some kind of sticky/oily substance that contains the poison--that way it stays on the tip, and sticks to the target. But a bullet, especially at close range, is likely to pass right through its target, unless it shatters on impact, like a hollow-point bullet. Thus, I imagine that poisoned ammunition would be expensive because it would need to be specially designed--to explode on impact, releasing the liquid contained in a hollow interior chamber.
Alternatively, if it's a weapon based on black powder, you could rule that the bullets themselves are coated with poisonous powder--safe for contact just with the skin, but dangerous if introduced directly to the blood stream. Kinda handwavey of the whole thing, though, in my opinion.
Of course, part of this also depends on the comparison between the pistol and a regular ranged weapon (presumably a crossbow). If it's substantially easier to use, with no need to gain proficiency or the like? Seems like making "poisoned bullets" semi-realistically difficult would be a good check. If the pistol is effectively identical to the crossbow (or some other regular ranged weapon) and is therefore just a change of fluff? Or, alternatively, if there's already been a good cost associated with it (e.g. paying a feat, or having ammunition be expensive as it is)? No real point making the poisoning hard/expensive to do on top of that.
