Grass/Ice
Water/Dragon
Water/Fighting
Grass/Ghost
Ice/Poison
Lots of good options here.
Grass/Ice: Easily the most on concept of the bunch. Grass typing grants Clamp resistance, Ice grants neutrality and immunity to being frozen by Cloyster's Blizzard, and STAB Razor Leaf threatens huge damage on Cloyster while being no concern to Articuno.
Water/Dragon: 4x resistant to Clamp, neutral to Blizzard, no weaknesses or OU relevant resistances. Overall, should be a good typing that mostly targets Cloyster.
Water/Fighting: It needs a boatload of Attack to threaten a 2HKO on Cloyser with High Jump Kick, so high that it is maybe too capable of hitting Articuno as well as distorting the metagame by being extremely potent against Chansey, Snorlax and Tauros. Although, it could maybe still go the Razor Leaf route to deal with Cloyster, with its Fighting-typing instead allowing for better overall stats/movepool to make up for being saddled with a Psychic-weakness.
Grass/Ghost: I really like this offensive-based approach to handling Cloyster with Clamp resistance/Explosion immunity, but its weakness to Blizzard could make switching into Cloyster too dangerous for it to function reliably as a Cloyster check.
Ice/Poison: An interesting typing with big drawbacks (Psychic/Earthquake weaknesses) that could justify handling Explosion with tons of physical bulk, due to an Earthquake weakness letting physical attackers muscle through without too much trouble. The lack of Clamp resistance is worrying, though. Cloyster could wear CAP down pretty fast this way, and its Special bulk can't be too high to mitigate Clamp damage or else Articuno will fail to beat this CAP like we want it to.
Water/Dragon
Water/Fighting
Grass/Ghost
Ice/Poison
Lots of good options here.
Grass/Ice: Easily the most on concept of the bunch. Grass typing grants Clamp resistance, Ice grants neutrality and immunity to being frozen by Cloyster's Blizzard, and STAB Razor Leaf threatens huge damage on Cloyster while being no concern to Articuno.
Water/Dragon: 4x resistant to Clamp, neutral to Blizzard, no weaknesses or OU relevant resistances. Overall, should be a good typing that mostly targets Cloyster.
Water/Fighting: It needs a boatload of Attack to threaten a 2HKO on Cloyser with High Jump Kick, so high that it is maybe too capable of hitting Articuno as well as distorting the metagame by being extremely potent against Chansey, Snorlax and Tauros. Although, it could maybe still go the Razor Leaf route to deal with Cloyster, with its Fighting-typing instead allowing for better overall stats/movepool to make up for being saddled with a Psychic-weakness.
Grass/Ghost: I really like this offensive-based approach to handling Cloyster with Clamp resistance/Explosion immunity, but its weakness to Blizzard could make switching into Cloyster too dangerous for it to function reliably as a Cloyster check.
Ice/Poison: An interesting typing with big drawbacks (Psychic/Earthquake weaknesses) that could justify handling Explosion with tons of physical bulk, due to an Earthquake weakness letting physical attackers muscle through without too much trouble. The lack of Clamp resistance is worrying, though. Cloyster could wear CAP down pretty fast this way, and its Special bulk can't be too high to mitigate Clamp damage or else Articuno will fail to beat this CAP like we want it to.