
Mr. Mime (F) @ Light Clay | Filter | Timid | Reflect | Light Screen | Dazzling Gleam | Psychic (Level 68)
Dual screens are a tried and true tactic for in-game Fairy specialists, dating back to the type's debut with Valerie, and since utilized by most of them at some point. (As a bonus, they're also the most iconic archetype of Monotype Fairy teams here on Smogon.) I'm probably only too pleased to persist in this particular tradition with the Pokemon most closely associated with the screens in terms of flavor.
All its in-battle details follow naturally, almost inevitably from the premise of a lead dual screens Mr. Mime. Light Clay boosts their duration, Filter boosts its ability to stick around just long enough to set both screens, a Timid nature aids that goal in another way, and then there's the STABs to complete the set Valerie pioneered ten years ago. Psychic also helps alleviate excessive vulnerability to one of Fairy's typical weaknesses.

Azumarill (F) @ Sitrus Berry | Huge Power | Jolly | Belly Drum | Play Rough | Superpower | Aqua Jet (Level 68)
Another very typical set, Azumarill sets up with much help from Mr. Mime's screens and then hopefully goes to town. There's not even much to comment on here, as the Sitrus Berry, Huge Power, Belly Drum, and Aqua Jet all clearly go together. Play Rough is a common choice too, locked in by being its Fairy STAB and on a team without other Play Rough users. Superpower is the only slightly unconventional move on its set; it's meant to solidify Azumarill as its team's answer to Steel-types, an otherwise poor matchup almost all around, while allowing trainers to play around the scary +6 Attack a bit. Meanwhile, the Jolly nature makes it more practical to utilize Play Rough and Superpower, which seems like the play for an in-game NPC's team.

Roserade (F) @ Focus Sash | Natural Cure | Bold | Attract | Swagger | Giga Drain | Extrasensory (Level 68)
I originally had Roselia in this slot to parallel Pikachu, but without Eviolite, it unfortunately offers nothing over its evolution in battle. At least Roserade adds a touch of refinement that's always been part and parcel of Fairy's flavor as a type, on top of its Shiny Stone evolution. In this team, its moveset now ties it more firmly to Mr. Backlot's properties, while allowing it to serve as a disruptor and another facilitator of its teammates.
Piece by piece, there's two items found on every single BDSP Gym Leader rematch team: Focus Sash and Life Orb, the former always on something frail. That fits Roserade here, particularly due to Swagger sharply boosting opponents' Attack, whereas Life Orb has some negative synergy with this would-be dual screens team. The item decision merely fed into its planned moveset this time instead of determining it, because said set is centered around the TM found in the Pokemon Mansion + one of two found at Amity Square, neither of which I had room for otherwise. The former, Swagger, secures this Roserade as specific to its origin, offsetting its evolution line being the only one that's not associated with Trophy Garden somehow. As for the rest, Giga Drain and Extrasensory synergize through their respective healing and flinch chance while utilizing Roserade's very high Special Attack more effectively than another superfluous Dazzling Gleam; the latter secures Roserade's role as the team's Poison check to boot. Natural Cure is its Ability of choice, one which also contributes to a subtheme of status resilience, while a Bold nature helps it stick around longer.

Pikachu (F) @ Light Ball | Lightning Rod | Naughty | Volt Tackle | Surf | Iron Tail | Volt Switch (Level 68)
Raichu would've more effectively leveraged the screens, but they're only one part of my theme here. Thank goodness for the Light Ball, because Pikachu is the one allowed in Amity Square, while Raichu takes a hard right turn away from typical Fairy-type design principles. Like Roserade, Pikachu attacks fast and strong, though it's higher on the risk and reward for a variety of reasons. Notable among them are its moves, of which the first three are firmly associated with Pikachu in particular, while the last one's TM is found at Amity Square - and it doesn't learn any Fairy-type moves useful for its role in BDSP anyways. Volt Switch rounds off the set by allowing Pikachu to pivot out of matchups its main three moves don't cover, while a physical-leaning set with a Naughty nature provides much-needed extra power in lieu of EVs. Surf and Volt Switch still ensure Lightning Rod's stat boost finds some use, sealing its slot over Static on this set.

Blissey (F) @ Chople Berry | Natural Cure | Bold | Sing | Soft-Boiled | Charm | Dazzling Gleam (Level 72)
What comes after successfully clearing the maids' challenge in the Pokemon Mansion? A battle with either a Lady or a Rich Boy, each of which has exactly one Blissey. Unfortunately, aces are always last in BDSP type specialists' lineups; hopefully this one's AI would tend to send out Blissey after Clefable gets KO'd regardless. At any rate, those battles are also where I took my moveset cues, just as with Clefable below. This one needed more alteration, though - in particular, Fling is workable by in-game rematch standards in tow with well-chosen items and actual Attack stats, so not on a Blissey.
However, Rich Boy Liam's Blissey does directly contribute Sing in the first moveslot, while Lady Celeste's Blissey adds Soft-Boiled in the second slot. Liam has Defense Curl in his third slot, to which the Fairy-type Charm is mostly an upgrade that also synergizes more effectively with Blissey's most practical Ability. Meanwhile, Celeste finishes things out with Psychic on her Blissey, which I've replaced with the Fairy-type Dazzling Gleam to replicate its anti-Fighting purpose - with prospects by in-game standards thanks to its Chople Berry, Bold nature, Charm, and potential screens.

Clefable (F) @ Leftovers | Magic Guard | Quirky | Metronome | Minimize | Moonblast | Cosmic Power (Level 74)
My starting point for this moveset was those of each maid's Clefairy in Platinum, with a view to shaping them into something suitable for a type specialist's ace. Hence, Endure had to go, also given that its purpose was to play into the challenge to defeat all five maids in a fixed number of turns anyways. Metronome, however, did not have to go! It simply needed more competitive trappings, such as the first maid's Minimize alongside Cosmic Power to enable the unfettered wagging of fingers. As for the clincher, the maids' Meteor Mash is also outdated and deserved to go in favor of another night sky-themed attacking move, a post-Platinum introduction that's quintessentially Clefable (Fairy in general too) and that the rest of the team misses out on. Moonblast also ensures not all its eggs are in one basket.
Even Clefable's move order stems from the aforementioned maids - Metronome first, then Minimize, then a conventional damaging move (Moonblast in this case), and finally a means to lessen damage (Cosmic Power in this case). It has a Quirky nature in order to reflect the, well, quirkiness of its strategy, while not reducing any of its stats since Metronome can do almost anything. Magic Guard prevents trainers from whittling it down with status, a protection I consider more important in enabling this double-boosting Clefable to do its thing than Unaware (and also more Fairy-flavorful). And of course, it's meant to stick around for a while, a goal which Leftovers most effectively helps enable.
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The levels emphasize Blissey and especially Clefable thanks to their ties to the Pokemon Mansion itself while generally conforming to BDSP standards for a rematch of a Gym Leader where it's found. Likewise for the inclusion of held items, Abilities, and natures even while excluding EVs. Their movesets are meant to be an order of priority where not otherwise stated, while Team Cherish's lineup order groups the Amity Square lines together after the regular Trophy Garden encounters after the other two Fairy-types. Nicknames would've been a very fun touch, but alas, one in-game precedent really isn't there for.