If you release 5 copies of the same Pokémon at the 'Release Kiosk' you will receive a Ticket for a Pokémon from the released Pokémon's evolution line. If you then release those Pokémon in the following combinations you will be able to get Tickets for completely new Pokémon including those that don't appear in the wild.

Articuno:
Pidgeot + Fearow + Jynx + Lapras

Cloak:
5x Mothim Burmy Sand/Trash

Cut Rotom:
Rotom + Leafeon

Darkrai:
Wash Rotom + Heat Rotom + Spin Rotom + Cut Rotom + Frost Rotom

Dialga:
Dragonite + Bastiodon + Lucario + Garchomp + Magnezone

Frost Rotom:
Rotom + Glaceon

Gastrodon West Sea:
5x Shellos East Sea

Giratina:
Gengar + Dragonite + Garchomp + Spiritomb + Dusknoir

Heat Rotom:
Rotom + Flareon

Manaphy:
3x Phione

Mewtwo:
Dialga + Palkia + Giratina

Moltres:
Charizard + Pidgeot + Fearow + Magmar

Palkia:
Blastoise + Gyarados + Dragonite + Empoleon + Garchomp

Phione:
Lapras + Vaporeon

Shaymin:
Arcanine + Charizard + Kangaskhan + Bastiodon + Arbok

Shellos West Sea:
5x Gastrodon East Sea

Spin Rotom:
Rotom + Jolteon

Wash Rotom
Rotom + Vaporeon

Wormadam Sand/Trash Cloak:
5x Burmy Grass Cloak

Zapdos:
Pidgeot + Fearow + Raichu + Electabuzz

To obtain the following special Pokemon enter the corresponding codes in the red box in the 'Stage Select' area (middle option or third from the top if you have a ticket and there are four options selectable).

Bibarel:
Enter the code 9236-7400

Charizard:
Enter the code 9600-4319

Cherrim:
Enter the code 1923-1298

Eevee:
Enter the code 5873-1954

Mew:
Enter the code 6614-0248

Ninetales:
Enter the code 6295-6406

Pikachu:
Enter the code 2110-9011

Rattata:
Enter the code 3884-9402

Rotom:
Enter the code 9966-1569

Zapdos:
Enter the code 8106-8836