Good question! And one every GM has to deal with from time to time I would think. I'd probably pick one or two of these:
Keep the pace. Part of your story revolves around urgency. Let them feel stressed out, make your encounters heave for breath, more so the closer the party gets to the final boss fight. Try to make them feel guilty for even the slightest pause, thorough searching etc.
Help them recover. Let the PCs discover an old and forgotten crate with a nearly empty healing wand, some crumbling restoration scrolls and a six-pack of useful potions with faded labels.
Surprise the badguys. Villains also need to deal with changing schedules.
- An important ritual component is lost or spilled on the floor during preparation and a minion is dispatched to the nearest town to procure more.
- A pair of blundering ogres accidentally discover the villains hideout and must be dealt with, depleting resources.
- A cloudy night sky diminishes moon power, so the ritual is postponed for a day or two until weather clears up.
- The players can mess up the villains schedule. Give them a chance to funnel a swarm of dire bats into the villains part of the dungeon, thus creating havoc and buying time.
That very much depends on what you mean by "in game."
During a game?
Certainly:
PC: "I fall on my sword."
DM: "Okay. You die."
Using standard combat options?
No.
At least, not guaranteed at every table by a common understanding of the rules.
Coup de grace requires that the target be helpless before it's an option, and whether you're helpless to yourself is going to split the audience of DMs down the middle, more or less. Some will say no, you aren't helpless to yourself ("heck, people flinch away from their own razor!"), and others will say sure, go ahead and coup yourself out.
The combat actions and options made available by the game just aren't intended to cover every possible violence that a PC could commit. If you're alone, just you and a basket of puppies, and you pick it up and hurl it over the cliff, do you have to roll initiative? No — there's nobody there to contest with for the initiative. There's no action involved that's combative. At most it's a skill check, if for some reason there's the possibility of fumbling the throw and not disturbingly dispatching the puppies. It's not even a coup de grace.
When you're dealing with a character committing suicide (for whatever reason), unless it's suicide-by-battle the combat rules aren't engaged by the action. It's just violence, tragic or senseless, committed by the character against themself, vetted by the DM as possible and properly executed, and observed by your fellow players as a contribution to the shared imaginary space you're all consenting to create.
Best Answer
Both 'Yes' and 'No' are reasonable and justifiable
As the other answers noted, sticking to the RAW, Pathfinder doesn't cover the simultaneous action required for multiple coup-de-grace attempts, but this is exactly the place for the DM to make a judgement call.
Without the simultaneous coup-de-graces, if the first strike didn't outright kill the monster, it will awake (grumpy and in great pain) - negating any further coup-de-grace maneuvers. This may turn into a redundant anti-climax as the other characters (with their delayed initiative) stab at the monster while it lies prone. So, if it'll probably die anyway before getting a chance to act, you can reasonably go with the dramatic instead of sticking to the mechanics of turn-based combat simulation.
On the other hand - consider the same scenario with an immensely powerful monster - such as a 200 hp purple worm, which fails the will save against Slumber at the beginning of combat (which is not unlikely, given it's +4 Will save). If you allow only a single coup-de-grace attempt, the worm has a fair chance of surviving it (a +17 Fort save vs. 10 + Damage inflicted), leaving the group to fight a grumpy purple worm, which in all likelihood will swallow the offender and poison at least one of his comrades on it's first turn. Allowing the whole party to "join the coup-de-grace party" will probably make for a poor alternative to an epic combat - or to some brilliant problem solving and role-play, as the PCs try to find a way to slay the worm without waking it first...
Finally, consider how you will handle a helpless player character at the mercy of, say, 10 kobolds (one of them a 2nd level Witch with the Slumber hex). If the PC survives the first coup-de-grace (3 x (1d6 - 1) for a kobold spear averages 7 hp damage and a Fort 17 save) it'll be much more satisfying for everyone around the table if he gets a chance to act, and kill his captors like a bad-ass, instead of having to suffer an average of 63 more hp damage and making 9 more Fort 17 saves before he gets a say.
Bottom-line: It all comes down to two factors:
On my current group, I'd probably allow this only as a time-saver when a single coup-de-grace will likely kill the monster anyway, but not against stronger opponents or against the PCs themselves.
Final Note: taking the time to tie the monster so it'll remain helpless even after the first coup-de-grace will solve this rules-wise, but only for opponents you can reasonably tie (excluding most strong and big opponents...)