Updated as per pg.72 Legend of the 5 Rings, 3rd Edition
Revised
GREAT CLANS:
Crab: Gunmetal Grey,
Blue, Brick Red
Crane: Sky Blue, White
Dragon: Emerald Green, Yellow
Lion: Gold, Earth Tones
Mantis: Sea Green,
Black
Phoenix:
Red, Yellow, Orange
Scorpion: Blood Red, Black
Spider: Black, White
Unicorn: Purple, White
Toturi's Army/Wolf Legion: Blue, Tan,
and Brown
Shadowlands: Fuschia, Light Green, Grey
MINOR CLANS:
Badger: Brown, Black
Bat: Black
Boar: Brown and Grey (I
might be wrong on this one)
Dragonfly: Blue, Brown, Gold
Fox: Brown, Green
Hare: Red, White
Monkey: Orange, Brown
Ox: Blue, Black
Snake: Green, Black and Purple
Sparrow: Shades of
Browns
Tortoise: Light Green, White
The Imperial Colors I am sure are Green and Gold, but they also they tend to wear a lot of yellow, brown and black since these appear to be the official 'unaligned' colors of Rokugan.
The Otomo also sometimes wear Dark Blue and Yellow, so maybe these are the family colors of the Otomo. Though this is taken from the card art of various Otomo family members. But all the card art of the others appears to be either green and gold or brown, yellow and black.