There are four abilities for Chocobo(and with it the colour)and must be obtained in order and they are all around Mist continent.
*Cross river(Blue) : Dig all ChocoGraph in ChocoForest(MiniMog will tell you when you 've done) ,there is one for the lacation of the first ability(disc 1).
*Climd muontain(Red)ig all ChocoGraph in ChocoLagoon,get second ability(disc 2 because you can only go to Forgotten Continent by aitship)
*Cross sea(Purple)ig all Chocograph in Forest(appear more after you get Second ability),get thirds ability(disc 3 ,I think you can't go to Forest in disc 2(?))
*Fly(Gold) ig all Chocograph in Lagoon(appear more after you get third ability),get last ability.(disc 3)
Now you can dig on Garden and complete Chocobo side quest.