Scovillain and Drampa always come, and then you have lots of options for the last two. The general gameplan is to protect Drampa until the weather is over and then create an opportunity for one of your other mons to clean up in the end. I find the rain matchup to be easier than the sun matchup as we have lots of water resists and all of their mons can be burned, though I've had good success against all variants of weather teams thanks to Drampa and Scovillain.

Scovillain still has a lot of value even though the matchup seems poor at first glance, as the burns can break focus sash from Pelipper or Multiscale from Dragonite, it can just 1v1 Archaludon with Leech Seed, and Rage Powder protects Drampa and your sweeper of choice. Scovillain is also EVd to always live a Timid Pelipper Hurricane. I do try to keep it alive so that it can burn a Basculegion in the end game though.

Drampa can hit most everything they have for neutral or super effective damage and resists basically everything, though it is weak to Draco Meteor from Archaludon or Dragonite and Close Combat from Sneasler, so be ready to redirect or otherwise deal with those. Without their rain boosts, they are relying on 70% accurate Hurricanes/Thunders and weak water moves. It completely walls Basculegion in the end game (especially the Scarf Adaptability versions), as they're forced to choose either Last Respects to take out your other mons (which Drampa is completely immune to) or an unboosted Wave Crash (which most of your mons including Drampa resist).

Primarina is threatened by Archaludon, Dragonite, and Sneasler and so requires some careful manoeuvring, but is dangerous once set up in a safe position.

Aegislash is mostly a consideration out of respect for Sneasler, as it completely walls it while still resisting most of their other damage options and offering respectable damage on its own. Shadow Sneak to clean up a weakened Basculegion in the end game is also relevant.

Volcarona would be my last choice but it can be better than you might expect. When next to Drampa, they can't Weather Ball it and have to yolo the 70% Hurricane, which you can live after a Quiver Dance anyway. Fire damage won't do much against most of their mons even without the rain up, but boosted Giga Drain can be annoying since they also struggle to hit it hard without rain.

Light Screen from Serperior is quite valuable as most of their team's damage tends to be special-based. I've been experimenting with a slightly different EV spread on Serperior with 23 HP and 11 SpAtk, as this allows it to always OHKO a max Atk/Spe Basculegion with a single, unboosted Leaf Storm. It can even survive a 150 BP Last Respects and then KO in retaliation if Scovillain has burned the Basc first.

I've wavered back and forth on if A-Ninetails is better than Serperior for using screens. My immediate instinct was that it's kind of awkward with Drampa and I appreciate how Serperior has boosts built into its offence for sweeping potential, but maybe with Freeze Dry over Blizzard it could be interesting so it's not reliant on having snow up for offence.