Koi are a species of fish (specifically carp) that live in ponds. They used to be bought as a pet in the Pet Shop. Wild Koi are not seen during the game, so it is unknown as to where the Pet Shop gets them, like the parrot. However, there has been a release of a Koi pond in the 2011 Earth Day furniture catalog. You need to buy the Koi Pond then hold it in the air then press the up key. Then koi will swim in it.
Players can also see the Koi in the pond during the play, "Fairy Fables", in their natural habitat.