Oh this is a really fun thread idea, I like this a lot.
I'm not sure if I'm meant to be a trainer or something like a gym leader or e4 member for this, but I'll go with the latter since that's easier. Also, this will be in a 6v6 doubles format. I don't see anything on the main post specifying that it has to be singles, so I think this is ok?
Also, note that my competitive experience is limited and I've never made a competitive team before, so there may be some really dumb decisions here.
Team:
Mawile, Gardevoir, Azumarill, Wigglytuff, Ninetales, Mega Altaria (I'm not sure how to add the gifs/sprites that people above have been using)
I don't feel like doing items, but I will do movesets and abilities.
Mawile:
Ability: Intimidate
Moves: Helping Hand, Fake Tears, Growl, Protect
tbh, Mawile's stats just do not look good, so fuck it, it can be full support. Helping Hand is a priority move, which is useful since both Mawile's speed and bulk sucks, and Helping Hand works well with a Fairy-based doubles team, since Dazzling Gleam is a thing. Fake Tears also goes well with 4 of the remaining five pokemon on the team being special attackers. Growl is for a pokemon later on. And of course, Intimidate decreases opponent physical attackers's strength.
Gardevoir:
Ability: Synchronize
Moves: Dazzling Gleam, Psychic, Thunderbolt, Heal Pulse
Gardevoir is a strong special attacker, Dazzling Gleam lets it hit both opponents with Fairy STAB, Thunderbolt is nice coverage, and Heal Pulse is a nice support move. Not much else to say here except that, due to being a Psychic type, it can use super effective STAB on Poison types, which is really nice for a fairy team.
Azumarill:
Ability: Huge Power
Moves: Liquidation, Play Rough, Aqua Jet, Protect
Azumarill is of course a strong physical attacker with Huge Power, and also the only physical attacker or water type on this team, making it a great offensive pokemon for the team. Aqua Jet is useful considering Azumarill's bad speed.
Wigglytuff:
Ability: Competitive
Moves: Dazzling Gleam, Nasty Plot, Blizzard, Flamethrower
Wasn't really sure what to do with Wigglytuff, I ended up deciding to just make it a special attacker with Nasty Plot and a lot of coverage, because it *does* seem like it has some potential special strength if you get it set up. Since it has Competitive as an ability, I also gave Mawile Growl so that it could potentially help Wigglytuff become much stronger much easier too. It's not using its attack anyway.
Ninetales:
Ability: Flash Fire
Moves: Flamethrower, Nasty Plot, Energy Ball, Dark Pulse
The only non-Fairy type on the team, because there are only five Fairy lines in ORAS. I always felt like Ninetales should have been a Fairy type though; it feels like a Fairy type, and Fire/Fairy hasn't even been used yet. It's even in the mini Fairy section of the Kanto Pokedex, in between the Clefairy and Jigglypuff lines, and its alolan form is a Fairy type. So I feel like it fits the Fairy vibe of the team. It's not just that though; It also has a very useful type for this team too. Fire does super effective to Steel types, and resists Steel attacks, which is valuable for a Fairy team that would struggle a lot with Steel types. This gives it a very important role of being a great Steel counter for this team. The reason I didn't give it Drought is because it would mess up Azumarill a lot, though it still could be an option as it would give it even stronger Firepower and Solar Beam. I used Dark Pulse as its final move because there's no other attacks on this team that hit Ghost and Psychic type super effectively, though other options include Will-O-Wisp to inflict burns or Extrasensory to make it simultaneously a Poison and Steel counter.
Mega Altaria:
Ability: Pixilate
Moves: Hyper Voice, Tailwind, Cotton Guard, Hurricane
The ace of the team, and one of my favorite Fairy types, Mega Altaria. Since this is ORAS, Megas can be used, which is nice because it means I can use Mega Altaria. Pixilate makes Hyper Voice an extra strong Dazzling Gleam, and Hurricane is a coverage move, as Flying isn't representated anywhere else in the team. I didn't bother using Dragon STAB, because none of the special Dragon moves seemed all that impressive except Draco Meteor, which decreases Special Attack heavily, and it's redundant on a Fairy type anyway (let alone a Fairy team). Tailwind also increases speed for the whole team, and cotton guard makes Mega Altaria's already good physical bulk a lot better.