Known Charm Sets

Pokedoll charm sets were released in small waves. Each set has a date listed on the back of the item or on one of the Pokemon if no item was included.

Umbreon/Grimer/Gengar/Pokedoll Tag- 2002
Pichu/Tufty Pichu/Houndour/Pokedoll Tag- 2002
Corsola/Togepi/Psyduck/Pokedoll Tag- 2002
Celebi/Espeon/Mew/Pokedoll Tag- 2002

Pikachu/Wailmer/Wynaut/Pokedoll Tag- 2003
Torchic/Treecko/Mudkip/Poke Ball- 2003

Rayquaza/Mewtwo/Salamence/Charizard-2004
Munchlax/Bonsly/Mime Jr./Weavile- 2005 
Pikachu/Charmander/Chikorita/Mudkip (Mystery Dungeon DX)- 2005
Rayquaza/Kyogre/Groudon/Master Ball- 2005
Lucario/Regirock/Registeel/Regice- 2005
Pikachu/Meowth/Mew/Poke Ball- 2005

Shiny Genesect/Genesect (Burn)/ Genesect (Douse)/Genesect (Shock)- 2013
Pikachu/Eevee/Dragonite/Oshawott- 2013
Venusaur/Blastoise/Charizard/Mewtwo- 2013

Jirachi/Darkrai/Manaphy/Victini - 2014
Dedenne/Chespin/Fennekin/Froakie - 2014
Pikachu/Charmander/Squirtle/Bulbasaur - 2014
Espurr/Meowstic (Male)/Meowstic (Female)/Sylveon - 2014

Photo by phoenixxfoxx

Photo by astron

I have been unable to document release dates for the following sets. If you own any of these charms with a year on it, please contact me so I can update the list! 

Meowth/Wobbuffet/Magikarp/Pokedoll Tag
Pokeball/Munchlax/Plusle/Minun
Cyndaquil/Phanphy/Pikachu/Poke Ball

Blaziken/Swampert/Sceptile/Poke Ball
Grovyle/Combusken/Marshtomp/Corphish (Mystery Dungeon DX)