Lots of Possibilities here. Let's look at it from a Combat perspective first:
A rogue. A lot of their things aren't combat savvy. They can do the thief thing, but, with a Sap and sneak attack, can put anyone down. Even snip the ends of arrows off, and try to make 'Subdual' arrows (There's some enchantments for weapons that'd allow this). If the rogue can't sneak attack them (Undead, Constructs, Elementals) then go ahead, beat them down. Undead are Allready dead. Constructs never lived.
Bard. See rogue above for skills; they could be more into influencing people, inspiring them, from a more RP point of view. The bard could simply heal/buff the party, and stay Out of a fight.
Cleric. See above for better examples, but a God of Peace would make sense, instead of the cases of perhaps Pure Evil (Outsiders, Undead, etc). In 2e, Clerics didnt' use sharp weaposn because they wern't supposed to spill blood (Insert rolled eyes here).
Wizard/Sorceror. There's a feat that allows you to convert all of your spell damage into Subdual damage. Although you have to be careful Not to overdue on the subdual (It becomes lethal after hitting 0), then go for it. A subdual fireball would definetly take out a lot of people peacefully. Even spells that effect people nonharmfully (Sleep, Grease, Charm, Hold, Slow, Fear, Dominate Person, Reduce, Ray of Enfeeblement, so on). IF someone is slowed, Reduced, or Weakened, then they're more then likely to give up (Or fight even harder, like a cornered animal).
Monk. They may be so fully focused on the purity of the body and the harmony of the universe, that they do not wish to tip the balance by killing. Attacking with Subdual attacks would equate this.
Paladin. In Forgotten Realms, there's a God of Healing, and Martyrdom, Ilmater. I once had a halforc paladin in the party, who delt with Subdual damage. He used a Big Warhammer, and subdualed. Except when the party came up against a vampire (He was a short lived character, sadly; very peaceful soul).