Maybe its just because I've had the privilege of playing with a couple of inexhaustible polemicists, but far too many negotiations wind up in one of two categories:
1) The PCs spent an hour of irl time badgering the NPC until they get their way.
2) The NPC puts their foot down (because they're a king or a God or whatever). The PCs badger them for an hour of irl time, to no avail.
In either case, I wouldn't necessarily claim that the PCs deserve their victory/defeat, nor would I claim it was fun for any party involved. Personally, I like both deserved outcomes and having fun. To that end, I've slapped together a rules-framework for how to handle negotiations, or to use the slightly more evocative term, PARLEY.
WHEN TO PARLEY
I designed these rules for a fairly narrow selection of situations. For their best application, both of the following should be true:
1) The PCs are trying to get something out of the NPC.
It could be a favor, a change of heart, shakedown money, whatever. The key here though, is that the parleying is inherently asymmetric. There's not really a fair way to have a NPC force a PC to do things their way, at least not via sub-games.
2) Its unclear how the NPC would respond.
If the PCs want the generous farmer to lend them a room for a night, just have it happen. If they're asking for an interest-free loan from the Dracolich, don't have it happen. Unless it makes sense. Basically if you can figure out how the NPC would respond in a couple minutes, don't bother with having a proper parley.
HOW TO PARLEY
You go around the table, having each PC make a relevant skill check. The party needs X successes before Y fail--HAHAHAHAHA SIKE. Never again 4e, never again. This is how you actually do it:
1) The NPC starts off at Resolve equal to their hp/life points/whatever. Once the NPC runs out of Resolve, the Players get what they're after. Did I steal the term "Resolve" from Griftlands? Did I, in fact, steal this whole parleying concept from Griftlands? Yes, yes I did.
2) Each PCs takes a turn (order decided by Initiative, or just go clockwise if you hate numbers) with which they can take a stab at convincing the NPC. There's a few ways they can do this:
-Intimidate: The NPC loses 1d8 Resolve, plus whatever bonus makes sense for your system of choice (attack bonus for GLOG, Intimidate skill from 5e, etc.). However, the NPC gains 1 Lost Patience. More on what that means later.
-Manipulate: The NPC loses 1d4 Resolve, plus takes X bonus damage from Manipulation for the rest of the parley, where X is your Deception skill/levels in Thief/whatever.
-Reason: The NPC loses 1d6 Resolve. Now you could add your Int bonus to this, to put it on better footing with Intimidate/Manipulate, but Reason already has a hidden diegetic advantage: it doesn't make the NPC dislike you in the long term.
-Deal: The NPC loses 1d4 Resolve, plus 1d4 for each significant offering (roasted newt, oath of fealty, etc.) I'd stay away from using money as an offering, as that's more in line with simply buying something from the NPC. If the PCs have enough money to do so, they shouldn't be bothering with any of these parleying shenanigans.
-Build Trust: Offer the NPC sensitive information (i.e., information that could be used against the PCs/their allies) in order to remove 1d6 Lost Patience.
-Inquire: This is sort of a catch-all for all the clarifying questions that come up in normal PC-NPC interaction (who are you, what do you want, what is that wizard doing here, etc.) Also used to learn the NPC's Stance. Again, more on that later.
Finally, the PCs can boost their damage via player skill. If they roleplay a bit of dialogue relevant to their approach ("I've literally killed a dragon," could work for Intimidate) then they role Resolve damage twice and take the higher result. Ditto if their roleplaying goes off of what another player has said. If they do both, just have them deal max Resolve damage. If this seems like it'd end the parleying pretty quickly, that's the point.
3) Once each PC has taken their turn--and this is terribly, terribly important--TIME HAS PASSED. This means random encounters, expending limited resources, having to refill the parking meter, etc.
On top of that, the NPC gains 1d6 Lost Patience, which functions as damage-reduction for their Resolve. With each round of parleying, not only are the PC's put under resource-pressure, but it gets more and more difficult for them to win.
WAIT WHAT ARE STANCES
So the NPC's take a pretty passive role in all this but in an attempt to make each parley more unique, every NPC has a Stance. These are passive abilities that bend all the rules I've laid out above.
Examples:
Short Fuse: +1d8 Lost Patience per round. Turn hostile if Lost Patience reaches their starting Resolve.
Suspicious: Immune to damage from Manipulate and Reason. 3 in 6 chance of this stance being removed by a PC Building Trust.
90% of the time, I'd expect a Stance to work in the NPC's favor. If they're sufficiently "naive" or "simple-minded," there probably isn't a need to parley with them; just give them a shiny gold coin and be on your way.
MY CONFESSION
This system is pretty rough, but I imagine anyone interested will end up hacking it to their liking anyways. There's certainty a lot of room to do so. Maybe I'll make a more polished version for Rats on a Stick or something. Who knows.