Hey guys,
I came up with the idea of playing a pacifist character that doesn't want to fight (or only treats it as a last resort)? He/She would rather focus on healing and buffing the other characters of the party, debuff enemies and/or play with the minds of adversaries to end conflicts peacefully. For that reason he/she would probably be a tanky spellcaster (correct me if I am wrong).

Can you think of a race-class-combination that would work best for that concept?

Thanks in advance.

Cleric. 

Spells like Sanctuary and Shield of Faith will keep you safe. I would recommend a domain giving heavy armour proficiency with good always-prepared buff/heal spells like Life or Trickery Domains. 

Short answer: Yes.

Long answer...:

It's possible, but it also depends on the group of people playing.

I'm watching a one-shot where the Half-orc Barbarian is the pacifist, and so far, it works thanks to a lot of creativity and cooperation from everyone (DM included).

I've read about a group that despises pacifist characters, expecting even a squishy support character to get covered in the blood of the enemies.

What works best is what works best for you. Many combos can achieve HP sponge-y healers/CCers, but most of them are played differently to achieve it. Some take some leveling to come into that role effectively. I wish I could suggest some combos, but my preference is more evasion/DpS than support. There will likely be responders with suggestions, though. Try them out and see how well they fit.

I’m actually playing one right now, he’s a bard who literally has no overt attack spells (vicious mockery being the only effective one I’ve used so far) but is mostly there to provide buffs for the party and negotiation power. He’s become the ‘face’ of the party and has talked their way out of several conflicts. It’s possible for sure and to be honest the most violent characters I’ve encountered have been clerics so, you’re not stuck playing a healer. 

Wizards can be built to be very effective in combat without any damaging spells. They lack healing, but have so many good control spells that they can stop a lot of damage from happening in the first place. They also have a lot of great utility spells, many of which are rituals, so you can also have spotlight moments out of combat. And since you will be avoiding combat/damaging enemies, having a large list of spells to choose from will allow you to be flexible enough to be useful no matter what the situation is.

If you want some healing, just taking a 1st level dip into either cleric or artificer (if DM allows Eberron content) could be good. You will also get shield/armor proficiencies and that always nice to have guidance cantrip. Going further than 1 level for either class will probably not be ideal since many of their later features are damage focused and you will delay your wizard spells.

I’m less familiar with bards (I personally am turned off by the base flavor of the class), but you could probably make a nonviolent bard work really well too. You can be the face, are a full caster, have bardic inspiration, and your magical secrets allow you to patch up any gaps in your build.

I would say that Bard and Cleric are the best classes when going for a pacifist player. They both have a range of non-violent spells that can be used creatively (with the help of the DM).

As for race, you would have to get creative with that. It all comes down to the backstory of the character, since any race can become pacifist.

This is literally the description of the Redemption Paladin

Clerics, druids, bards, and artificer can fit a pure support role. But I don't really recommend a non-combat PC. That is what NPCs are for.

Maybe if you chose to specialize in damage types that didn't necessarily leave visible wounds (radiant, psychic, force, poison, thunder, necrotic (some might depend on DM)). That would be both flavorful and not a hindrance.

Absolutely possible, and cleric is a good class to go with, though bard also works well.

I think one thing you'll wind up doing, as a pacifist healer, is readying an action-- if you're up high in the initiative order, and no one is really hurting, but you're next to someone who's engaged in combat, if you think they might take a big hit in the round, you can say you want to ready a healing spell and then not use it until they take that hit. It means if they don't take damage, you're not really using your action that round, but it's a possibility, if you have some healing spells but not as many useful buffing spells. You can also ready yourself to dodge, so that you get an advantage against being attacked.

It's also possible to specify that you're doing non-lethal damage, if your character winds up in a spot where they run out of options.

Quote from CatDetective >>

It's also possible to specify that you're doing non-lethal damage, if your character winds up in a spot where they run out of options.

 Just note, I believe by raw it's just mele attacks that can be non lethal. If you want to Homebrew there was a magic item option in dnd 3.5 that made your wep nonlethal that you could use for inspiration