As with most other Pokémon games, Time and Darkness do have Pokémon obtainable only through an event. Luckily, you don't need to go to an event in Time and Darkness, as they use Wonder Mail Codes to unlock dungeons, and therefore, Pokémon!
The game has eight dungeons only obtainable throught these special Wonder Mail. At the end of each dungeon, is a boss Pokémon, usually a legendary, such as Rayquaza.
To use the Wonder Mail, just start up the game, and on the Main Menu, go to Wonder Mail, and insert the password. Here are the dungeons, with the password included.

 Bottomless Sea

Boss: Kyogre

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
FN01 HWN- 00%F
8678 +XY@ &%#3

Job Description: Get to the end of the Dungeon.

Job Reward: Aqua Harmonica - Increases Recruit rate for Water Types

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 Shimmer Desert

Boss: Groudon

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
#&S6 NY2& YJN=
1P57 F0MN MH7Y

Job Description: Get to the end of the Dungeon.

Job Reward: Terra Cymbal - Increases Recruit rate for Ground Types

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 Sky Stairway

Boss: Rayquaza

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
HW+8 66%T 5S51
+J5Y 4-K# H@P-

Job Description: Get to the end of the Dungeon.

Job Reward: Flying Pianica - Increases Recruit rate for Flying Types

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 Mysterious Jungle

Boss: Mew

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
X%8S WYY+ S-JF
PFH@ @##K 5W8K

Job Description: Get to the end of the Dungeon.

Job Reward: Grass Trumpet - Increases Recruit rate for Grass Types

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 The Great Hole

Boss: Giratina

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
WNWY JXTK &5C1
4N3- P4NM 8K&C

Job Description: Get to the end of the Dungeon.

Job Reward: Rock Megaphone - Increases Recruit rate for Rock Types

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 Giant Volcano

Boss: Heatran

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
FH0T HYNH R0QF
86N8 +SY@ &%YN

Job Description: Get to the end of the Dungeon.

Job Reward: Fire Drum - Increases Recruit rate for Fire Types

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 Mt. Avalanche

Boss: Articuno

Unlock Requirements: Unknown. Probably beat Darkrai.
Enter this Wonder Mail Password:
4MP= K98# CT%Y
R@-- &P7% %K86

Job Description: Get to the end of the Dungeon.

Job Reward: Ice Flute - Increases Recruit rate for Ice Types

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 Labyrinth Cave

Client: Shinx
Difficulty: C (20 Points)
Boss: Gabite

Unlock Requirements: Complete Chapter Ten.
Enter this Wonder Mail Password:
78SR -H2M P0+4
Y6FY 1&Y+ #R9S

Job Description: After you accept this job in your Job List, a new dungeon will be unlocked; Labyrinth Cave. At the 10th floor, you will fight a Gabite. Usually on the second or thrid turn, he will use Sandstorm. Bring a ground type to avoid the damage inflicted. At the end, he will give you the Gabite Scale. Give it to Shinx, and he'll give you the Luxray Fang.

Job Reward: Luxray Fang

Fight with Gabite

Mission

Also, there Pokémon that are non-legendary, which can only be found in these dungeons. Below is a list:

Sprite Name Type
Treeko
Only if not picked as starter or partner at start of game.
Grass
Grovyle
Only if not picked as starter or partner at start of game.
Grass
Sceptile
Only if not picked as starter or partner at start of game.
Grass
Gastly Ghost & Poison
Haunter Ghost & Poison
Gengar Ghost & Poison
Ekans Poison
Arbok Poison
Ditto
Normal
Diglett Ground
Dugtrio Ground