Murdering people for money? That's an evil act in my books. If the PCs are hired as hitmen and follow through, their alignment goes south for the winter.
Alignment-wise? Well, not as written - the Assassin PrC as written pre-supposes that the character is a member of an organisation of paid killers. Switching from "kill solely to become an assassin" to "kill to join the assassins" is a pretty trivial change - the character has still taken the choice to join an organisation that kills for money, and that's pretty clearly Evil.
Pathdfinder Good Versus Evil said:
Good characters and creatures protect innocent life. Evil characters and creatures debase or destroy innocent life, whether for fun or profit.
Good implies altruism, respect for life, and a concern for the dignity of sentient beings. Good characters make personal sacrifices to help others.
Evil implies hurting, oppressing, and killing others. Some evil creatures simply have no compassion for others and kill without qualms if doing so is convenient. Others actively pursue evil, killing for sport or out of duty to some evil deity or master.
People who are neutral with respect to good and evil have compunctions against killing the innocent, but may lack the commitment to make sacrifices to protect or help others.
There's two aspects here. First, Good protects innocent life, and Neutral has compunctions against killing the innocent. So that's the basic "killing for money is evil" clearly falls.
But we're discussing the character who refuses to kill the innocent. Perhaps he only takes hits on those proven to have committed evil acts themselves. Maybe he actively Detects Evil before he will kill the target. Perhaps he kills for something other than personal remuneration.
Good still implies respect for life. Killing is a last resort. Of course, that also should apply to any form of combat. That would mean taking prisoners where possible,
stabilizing or
healing downed opponents to minimize loss of life, perhaps striking for non-lethal damage where this is practical. How often do we enforce that respect for life?
Finally, of course, we get to those entities who are not, perhaps, considered "life", such as the Undead and otherplanar creatures. A PrC that teaches assassination techniques which are to be used only against such targets, and only the evil ones, could justifiably be "Fantasy Good".
Here's a question for you: in "Batman Begins", Bruce Wayne has received training by the League of Shadows, but to formally join he has to kill a guy. It's basically the exact same entry requirement, and he refuses.
Now, in game terms, does BW qualify for the "League of Shadows" PrC by virtue of having received the training, or does he fail to qualify because he doesn't truly enter the order? If he doesn't qualify, does that mean he has some other PrC that is almost entirely identical, but not quite?
What I'm getting at is this: PCs are pretty much exceptional by their very nature, in just the same way as Bruce Wayne is exceptional. So, while I wouldn't replace the general "must be Evil" rule with a looser "must be non-Good" rule, if the player was able to present a strong in-story argument for his character being an exception to that rule, I would at least consider it.
And then, being me, I'd probably say "no". But I would at least
consider it.
Your scenario posits obtaining the training first, then being instructed to kill the person as a requirement of joining the organization. But he's already received the training. Doesn't that mean he's already gains one or more levels in the relevant PrC? The fact you can't take a level in Assassin before you meet the prerequisite of killing a person solely to become an Assassin seems to imply you get no training before you make that kill, differentiating this from the Bruce Wayne example.
This also comes back to the nature of prestige classes. The original theory - special classes intrinsically linked to the game world and organizations therein - faded pretty quick in favour of "options to better optimize my character and screw the backstory fluff - gimme my mechanics!".
Now, what if that evil PC with a few Assassin levels sees the light. He WAS evil, and he DID kill a person just to join the organization. Maybe he's killed a lot of innocent (and non so innocent) people since. But he's changed. He's come to respect life, and recognize that his past has been wrong. He was Evil, but his alignment has shifted, perhaps gradually or perhaps suddenly, to Neutral or even Good.
The Assassin abilities look a lot like learned skills - many are shared by other classes. Maybe the "can't raise" abilities are backed up by some evil power, or maybe they are learned techniques closely guarded by the Assassin organization. If he's no longer Evil, he probably no longer works for the organization and no longer receives training. That sounds like he can gain no further levels in the class, but there's no reason he would not retain his class abilities (possibly with the exception of the "can't raise" ones, if you view those as gifts from the Death Gods rather than learned techniques).
Like a Paladin, this character could "Atone" and return to Evil, and the organization, by proving himself loyal, and could then gain levels in the PrC again.
That alignment change would seem to be the crux of the unusual nature of the player character.
If we want to simulate the Bruce Wayne approach for the Assassins, it seems like that could be done in a role playing setting. But it's not as easy as getting the training, then refusing the final test. Here, it's a preliminary test, so it precedes the training. Other than, arguably, the "no raise" abilities, there's nothing supernatural about the assassins. The player needs to (in game, I expect) trick the Assassins into believing he killed that victim, but not actually have done so. Then he has to keep up the bluff, somehow avoiding assignments to kill on a non-Good (or non-Neutral, as the case may be) basis.
That would certainly require some pretty fancy footwork - accomplishing something truly exceptional. But you want your PC to be exceptional, so play it out in game and show that PC's exceptional nature.
The second option, of course, is a PrC that fits into YOUR game world, provides the same or similar training, and does not require killing a person to join. Perhaps it has some other prerequisite related to the purpose for which this organization has developed these techniques, and shares them with its initiates. IOW, re-skin the PrC - it doesn't have to be called Assassin - perhaps this is the Holy Inquisitor, rooting out the greatest of Evils and purging them as part of the Church's Holy Work. Maybe you require the ability to Detect Evil and Smite Evil, and a demonstrated dedication to the Holy Precepts of a very Lawful Good church to even be considered for this training. There's your "Paladin-Assassin" - assuming you wish to allow for same.