To get a mountain (green) or River ( blue) chocobo you need to mate a great or a good chocobo using the carob nut. You can't buy the carob nut in a store, instead you'll need to steal it from from the vlakorados that roam the woods near the bone village. You can always increase your chanced of breeding a speical chocobo if the parents are both S racers.
The mountain-and-river (black) chocobo is created when a mounting and river chocobo mate using a carob nut. Again, it's not absolute, but you can increase your chances of obtaining a black chocobo by training the mother and father hard.
Only you have a black chocobo, you can attempt to breed the ultimate chocobo. These gold chocobos can go everywhere. Have the black chocobo mate with a wonderful yellow chocobo with a zeio nut. These nuts are the rarest of all nuts. They can ONLY be found on a small island northeast of chocobo ranch. Note: however, that there are creatures in woods known as goblins. You should be able to steal the zeio nut from them during a battle.