I like the idea of a skill like this. Not only would it give more value to the Charisma stat (which otherwise is only really useful for reducing shop prices if you're male, and improving chances of pets/companions obeying commands), but it would also provide further ways to successfully survive in otherwise dangerous situations, especially if you're trying to be Lawful.
It could also be given a further boost to chances if wearing "of leadership" items or the necklace of the silver tongue. Furthermore, it could passively increase chances of successfully offering peace to a scared NPC. "Persuasion" is a poor choice of name, as it overlaps too much with Haggling in concept. "Diplomacy" works a bit better.
As for uses in quests, here are the quests I'd like to see it used on (just to give ideas if this is implemented):
* Raider Lord quest - defeat his band, but not him. Use Diplomacy on him. Three possible results - He's convinced to turn himself in, he's convinced to leave and never return, or he refuses to listen. If he turns himself in, which requires a "perfect" roll (and therefore would be rare), you get a special message not unlike how handing his corpse to the Sheriff gives a special message, and some additional reward from the Sheriff. If he is convinced to leave, he will drop an item that can be used to prove to the Sheriff that you drove him away, which will net the usual reward... but alternatively, you can keep the item and use it (since it would be quite a nice item). If you fail the roll, he will refuse to listen, and you must defeat him.
* Ratling Rebel's quest - rather than killing Dak, you use Diplomacy to try to convince him to cease using non-humanoids in the Arena (the humanoids can give their permission). This will satisfy the Ratling Rebel's quest, but will result in a lawful boost rather than drawing the PC towards Neutral. It will also significantly reduce the rewards from fighting in the Arena. Using it prior to the 20th fight will prevent the PC from obtaining the golden gladius - the reward will instead be a swift eternium long sword (thereby providing an item that is somewhat better than the gladius in terms of basic attacking quality, but still subject to some destruction effects and without the ability to get Tactics from Bart). Note that you only get one attempt.
* A new quest of some sort. Could perhaps also provide a way for characters without Diplomacy to get it.
I'm not sure I like the idea of having it used on Hotzenplotz, because he's not just a criminal, he's a crime lord. He has used Diplomacy, himself, to build his empire. He wouldn't turn himself in just because of Diplomacy and a show of force against his bouncers. On the other hand, I would like to see a way that Hotzenplotz can be brought to justice without being killed.