First off, you could just do the resistances and weaknesses with new rule paragraphs about Pokemon creatures and stuff.
Pokemon Type Colors
So, Pokemon has an own Card Game of course and you could just add in the brown fighting into red, but that would not really fit the color pie obviously.
I even thought about that myself and that is where I got to:
Normal is obviously colorless.
Fighting is about the fury of punching your enemy, that would be red.
Flying is a tough one, because it is either the Freedom (Red) or the Sky (White), I tend to bring it into White though.
Poison is about long lasting nasty damage effects, so it is Black.
Ground is either red because of the Mountains being the red symbol, or simply Colorless. Colorless is my personal favourite here.
Rock is the Hardness of Physical attacks, so it is Red.
Bug is Green - because Bug.
Ghost is either Black or Colorless, I would rather go with Black here.
Steel is either protection (White) or modern machinery (Blue). I tend to call it White, because Pokemon are no machines.
Fire is... well, guess. Red.
Water, even though it is not really fitting blue in a Knowledge way, it is a slow building and then booming Type, which fits Blue.
Grass is Green because of Nature and Growing and such, so it is Green.
Electro is tough again. It is either Modern Warfare (Blue) or Static Protection (White) or it is none of all (CL). I go with White IMO, but it is close.
Psychic is Blue because of that Magical thingy about it.
Ice is Blue just because Ice. It would rather be colorless, but Blue needs some Types and it is frozen Water. But it rather fits Colorless, I know.
Dragon is... guess, tough. They spit fire (red), they are superior creatures (green) and they know a lot of stuff (blue). I mostly go with Red.
Dark is Black obviously.
Fairy, the 6th Gen newcomer, sounds like a Green type so far.
Full list again:
COLORLESS
Normal
Ground
RED
Fire
Fighting
Rock
Dragon
BLUE
Water
Ice
Psychic
GREEN
Grass
Bug
Fairy
WHITE
Steel
Electric
Flying
BLACK
Dark
Ghost
Poison
Hope I could help you =)