Visual novels: Saya no Uta is pretty goddamn morbid. ...no seriously, it's a plot point to simply "be" like that.
Nier (not PSP... but not many "dark" PSP titles... because otherwise, aside from a few minor additions, and old, Breath of Fire V and the SMTs was the last that I can really say stuck to memory)
Can't let the lack of emphasis cause this one to slip by so I'm seconding Nier.
It's very much like a darker version of LoZ: Ocarina of Time (although I'd probably describe it as morbid rather than dark). But it also has excellent dialog, great characters, a wonderful soundtrack, and serviceable gameplay. There is a female character as well (although strictly non-playable though also not retarded either) that, despite appearances, is actually quite good and comes in early enough that your friend might have a chance to relate. But a few things I should note about the game...
1)Try to avoid the opening movie or looking up too much about the game. A lot of promotional material let slip some really big whoppers in terms of spoilers.
2)Ignore trying to get full 'chieves or trophies. This game was designed by the dev team formerly known as Cavia who are infamous for being colossal trolls to gamers. If a sidequest seems to require more effort to complete than its worth then it's probably worth ignoring.
3)For the love of god, LOOK AT YOUR MAP!!! Seriously, the RED X is your guide. Don't be a retard who spends 40 hours futility trying to complete a quest in the wrong fucking place and then bash the game because of your own mental deficiencies.
&4)The developers may be colossal trolls but they wont make it impossible to unlock all four endings. Everything you need will be provided for you. Only the optional stuff will require watching out for, and even then there is a NG+ feature in the game so either way don't worry about it.