I might be arguing for something different than your principle of charity. What I am arguing for - and I realize now that I haven't actually explained a procedure, just motivations for one - is along the following lines:

When somebody says something prima facie wrong, there are several possibilities, both regarding their intended meaning:

• They may have meant exactly what you heard.
• They may have meant something else, but worded it poorly.
• They may have been engaging in some rhetorical maneuver or joke.
• They may have been deceiving themselves.
• They may have been intentionally trolling.
• They may have been lying.

...and your ability to infer such:

• Their remark may resemble some reasonable assertion, worded badly.
• Their remark may be explicable as ironic or joking in some sense.
• Their remark may conform to some plausible bias of reasoning.
• Their remark may seem like a lie they would find useful.*
• Their remark may represent an attempt to irritate you for their own pleasure.*
• Their remark may simply be stupid.
• Their remark may allow more than one of the above interpretations.

What my interpretation of the principle of charity suggests as an elementary course of action in this situation is, with an appropriate degree of polite confusion, to ask for clarification or elaboration, and to accompany this request with paraphrases of the most likely interpretations you can identify of their remarks excluding the ones I marked with asterisks.

Depending on their actual intent, this has a good chance of making them:

• Elucidate their reasoning behind the unbelievable remark (or admit to being unable to do so);
• Correct their misstatement (or your misinterpretation - the difference is irrelevant);
• Admit to their failed humor;
• Admit to their being unable to support their assertion, back off from it, or sputter incoherently;
• Grow impatient at your failure to rise to their goading and give up; or
• Back off from (or admit to, or be proven guilty of) their now-unsupportable deception.

In the first three or four cases, you have managed to advance the conversation with a well-meaning discussant without insult; in the latter two or three, you have thwarted the goals of an ill-intentioned one - especially, in the last case, because you haven't allowed them the option of distracting everyone from your refutations by claiming you insulted them. (Even if they do so claim, it will be obvious that they have no just cause to be.)

I say this falls under the principle of charity because it involves (a) granting them, at least rhetorically, the best possible motives, and (b) giving them enough of your time and attention to seek engagement with their meaning, not just a lazy gloss of their words.

Minor formatting edit.