Q:

How should a DM resolve a smooth-talking player with a weak Charisma score PC?

This is an old problem, but one I am curious to find an answer to. 
One of our players is naturally a smooth talker, and his personality allows him to talk his way out of situations on the spot, and he does this in his daily life. The issue lies in that his character has a Charisma score of 9, which is a -1 modifier.
Not speaking poorly about our DM, as I wouldn't know how to resolve this dilemma either, almost every situation that should have called for a Charisma check with his character was resolved by his own natural ability to charm, sweet-talk, and work his way out of nearly every situation, completely ignoring his PC's terrible Charisma score. 
Granted, some of these he did have to roll for a check, and lost some and won some, and again, it's the DM's call. I'm just curious if there is a better way of resolving a situation such as this. 

A:

This is a delicate thing to pull off as a GM, because it involves finessing the subtle aspects of a player's agency vs the rest of the imagined world.  
The usual model of player agency is that the player has agency as far as their character and character actions are concerned, while the GM has agency for everything else in the world.  It's a good model and very rarely needs to be more sophisticated than that.  But that simple model pointedly ignores the character statistics, which I think are best conceived as an interface between the character and the rest of the world. 
For physical stats (strength, or combat skill) this is obvious, easy, and uncontroversial:  If a player tries to do something absurd, the GM need not even roll.  If a player tries to do ordinary things that are out of his class, the GM can simply roll and the dice will enforce things. 
The social or mental stats are tougher, but it is perfectly legitimate in my view for a GM to interpret the combination of a character's low charisma and a player's silver tongue as "That sounded better in your head than it did out loud."  Or specifically, the player's words may sound great, but they are just as aspirational as the player of a low strength character resolving to break down a sturdy door.  The character's words are filtered through low charisma and come out less effectively for whatever reason.  
(This is directly inspired by the Amber DRPG concept of "good stuff" and "bad stuff" but I have found it works just as well in D&D type systems.  I am quite sure other people have arrived at this approach without ever having seen Amber DRPG.)
There are several pitfalls:
First:  It takes consistency.  If, as a GM, you half-ass it, you will just confuse your players.
Second:  It helps a great deal to explain this technique to the players the first few times it comes into play, and to remind them occasionally.  If you don't, you can be perceived as a total flake of a GM, or worse, be perceived as playing favorites.  
Third:  It can be jarring or grating to players who aren't used to it, especially if they are in the habit of treating some of those stats as 'dump stats.'  It also, to be fair, steps up real close to the agency boundary surrounding the characters, which is often very sensitive. 
Fourth:  The players may want to turn everything into a die roll, instead of letting the GM more flexibly and creatively apply his or her interpretations.  Resist this; the GM is under no obligation to let the players call the shots for when dice are rolled.
Fifth:  I shouldn't have to say this, and it is directed to the ghosts of my gaming past more than anything else, but-- resist also the urge to humiliate your players.  A charisma of 9 or a penalty of 1 is not crippling.  Even a stat that genuinely is crippling is often best glossed over rather than rubbing the player's nose in it. 

A:

From the description of Charisma in the Basic Rules:

Charisma measures your ability to interact effectively with others. It includes such factors as confidence and eloquence, and it can represent a charming or commanding personality.

You can say the sweetest laced words in the world, but if you say them condescendingly or without the presence to gain people's attention it wont amount to much. 
As a DM, I would have him define the mannerisms of his character to reflect why he has a 9 charisma. Does he say smooth things but mumbles them so no one can hear them? (Gordon Agrippa from Black Clover is an excellent example of this type of character)
Or does he say them in condescending ways? Much like how a high elf would talk to/about a dwarf. Characters with a 9 charisma have some sort of personality flaw that slightly detracts from their interpersonal skills. You can try having your DM implement a rule that you can dictate what your character says, but your Charisma roll reflects HOW he says it. 
You can call a King a fool with a charisma roll of 20 and he will think you a jester and laugh, but just try calling a King a terrific ruler with a charisma roll of 1 - he will think you are trying to insult him in some way and have you arrested!

A:

Resolve it the same way for all player/character disparity. What's written on the character sheet takes precedence
Players don't have to be strong or dexterous to play characters with high STR and DEX. They don't have to know how to skin an animal or track game to play a character with Survival proficiency. Most obviously - they don't have to be able to do magic to play a spellcaster!
To determine success in a challenge, the numbers on the character sheet have higher precedence than player skill. 
If a player who is really bad at tactics is playing a character with a lot of skill in that area, the GM should take the horrible plans the player comes up with and assume that the character has a good plan. 
It works the same the other way, though this requires a fair amount of trust at the table. If a player comes up with a great battle plan but their character is unskilled then the GM should take the great plan and have it fail in some way, to reflect lack of character skill. This has to be done delicately, and consistently, to avoid hurting feelings.
Another option is that when one player has a cleaver idea that their character probably wouldn't come up with, let the characters of other players use it.
My experience
I've been in two games with exactly this situation.
In one case, the player wasn't aware they were doing this and a quick OOC conversation sorted the issue. "Hey, Bob, I know you are a smooth talker but your character isn't, so please don't get upset when your character flubs conversations." 
In the second case, the player was doing it deliberately and had done so in previous games (board, card, and rpg). The conversation at the table got heated (as if often does when you call out a manipulator) and ended in the player leaving. It was upsetting at the time, but in hindsight it was the right thing to do. 

