Note:

There is another way to do this. Defeat the Ruby WEAPON. You will get a desert rose. See my Tips, Tricks, and Secrets page, and click on the link titled "The Man In Kalm"

Once on the second disk with the Highwind and Cloud in your party, this will mean something to you. Buy 99 of the cheapest greens in the Chocobo ranch (Gysahl Greens, I think). Buy as many stalls as you can afford. You'll probably need all six in a while. Equip a Chocobo Lure on someone and head down to the sourthern island of Mideel. Find the Chocobo tracks and look for a chocobo accompanied only by Spirals, the little purple things that look like an oversized bug that rolls in a ball. These will now be known as Great Chocobos. Catch a Great Chocobo. Now go to Gold Saucer Area Chocobo tracks. Here, you will have to catch Good Chocobos. If they appear with Flap Beats, they have to be in front of them. Also, other winged creatures that come can be in front or back of them. Get at least three of these Good Chocobos to make sure you will get the right gender. Now go to the Chocobo Farm. (SAVE OUTSIDE FIRST!) Ask the guy to move your new Chocobos in. What we want is a Male Good and a Female Great, or a Male Great and a Female Good. Either one; it doesn't matter. Once you have the right pair, release any others you may have. If you don't have a good pair, reset, and enter the Farm and try again. See why I made you save it?
Now, hop in the Highwind to the Chocobo Sage's house. He can be found in the middle of the snowy land on the top left of your map. (Talk to the Green Chocobo to get an Enemy Skill Materia!) Talk to the guy, and buy 99 Sylkis Greens. If you have W-Item, buy 1. Do the code back at my Codes page until you have 99. Okay, go back to the Farm, and as always . . . Save it outsite first! Give 50 greens to of you Chocobos and 49 to the other. Because now, we are off to the Chocobo races. Talk to Ester in the top left corner and choose either one of your Chocobos. Short races are the best. If you want to cheat (and why not?) hold R2 and R1 and your Stamina should rise. Win 9 times total for both of your Chocobos to get them to Class S. There is a Black Chocobo named something like Teioh, and you'll probably have to be pretty lucky to beat him. Once both Chocobos are in class S, save it, and head for Bone Village in the north, but don't go in. Stay on the World Map and walk around. Get in a fight with a red dragon-like creature named Vlakorados. One Vlakorados has only one Carob nut, but fight enough to steal about three or four Carob nuts. And if you have Morph Materia, you can Morph Vlakorados into an Elixer! Oh, and if you do not have your Steal Materia, don't worry. Go to the Gold Saucer. Go into the Wonder Square. You can exchange 500 points for a Carob Nut. But you may be thinking "500 POINTS!" Well, first see my Codes page, and see the tip called "The Man At Gold Saucer." And another thing, when racing your Chocobos and you win, unless you get some really good item, take the GP.
Go back to the Chocobo Farm, SAVE BEFORE YOU ENTER! Because now, you are trying to get a special Chocobo. Talk to Billy and tell him that you want to mate your Chocobos. Choose your CLASS S Male Good and Female Great (or vice versa) and mate them with a Carob Nut. You should get a blue, green, or yellow Chocobo. If you get a blue or green, go outside and save it. If you get a plain ol' yellow Chocobo, reset and try again.
Once you have one of these special Chocobos, go explore around for a while, or raise your stats, (you cannot breed again for a while) maybe near Mideel. If you have Gil Plus Materia (found at the Gold Saucer Wonder Square for 100 GP) go to the little island close to Mideel. Walk along the coast and you should always fight Sea Worms. With Gil Plus (I think this is only with a Level 1 Gil Plus) you should get 10,000 Gil a fight!! That could help extremely! Or better yet, if you can go into the Crater, go as far as you can. In one area you will fight Magic Pots, the little pots with purple dudes who stick out and say "Gimme an elixer!" You should be able to Morph Master Tonberrys (they have stars over their heads) into elixers, or you can Morph Vlakorados into elixers. Use the W-Item duplication trick and get 99 elixers. You should get 1,000 AP (I think) for defeating ONE Magic Pot! (note: you can only defeat them by using elixers!)
Well, once you are able to breed again, (I cannot stress how much you must SAVE BEFORE TRYING!) breed your two Class S Great and Good Chocobos with a Carob Nut. Cross your fingers and you should get the other (blue or green . . . make sure that you have both!) kind of the opposite gender. If you don't, try again, for now, we want to get a Black Chocobo! Once you have both Green and Blue (mountain and shallow river) Chocobos, go buy 99 Slykis Greens and give one 50 and the other 49. Next, take them to the Gold Saucer, because, we're going to race our new Chocobos to Class S! Win 9 times to get to Class S. When you're finished, head over to the Chocobo Farm and, you guessed it, SAVE FIRST! After you save your game, go inside and tell the guy that you are ready to mate your Chocobos. Make sure that they are Male and Female Class S Green and Blue Chocobos and choose the Carob Nut. Cross your fingers for a Black Chocobo (mountain and shallow river). If you don't get it, reset and try again until you do.
Now, before you think that you should raise your stats, head over to the continent at the top of your map (the snowy one) because now we are trying to get a Wonderful Chocobo. The only good ones here are the ones with bunnies. They can be in the front, back, one bunny, two bunnies, just some bunnies HAVE to be there. But it can only be bunnies, not any other enemies! Catch at least three to make sure that you have the right gender, and head back to the Chocobo Farm. SAVE BEFORE ENTERING (as usual) and check to see if your Chocobos can mate yet. If they can then it is time to hop back into the Highwind. Head to the small continent above the Chocobo Ranch (look on your map) so you can get a Zeio Nut. Fight the little imp-like dudes (known as Goblins) and EITHER steal the Zeio Nut OR you might be able to win it by defeating them. Once you have at least one, go back to the Farm (you might want to save it again) and feed 50 and 49 Sylkis Greens to your Wonderful and Black Chocobos and race them up to Class S. Once you have completed racing, head back to the Farm to breed. SAVING wouldn't be that bad of an idea. (I know, I really like to save a lot) Use the Zeio Nut with the Wonderful and Black Chocobos and hope for . . . THE GOLDEN CHOCOBO!!! (It can travel on land, mountains, water, ANYWHERE!!!)
Remember that the Golden Chocobo has a strange orange-like glow, you can't miss it. Once you have a Goldy, you can visit the Materia Caves to get some very nice Materia.
Another thing, for every new Chocobo born, if it's parents were at Class S, it will be a little bit faster than normal, and you'll have a better chance to get a special Chocobo.

Congrats, you should now own a Golden Chocobo!!!

NOTE: If something doesn't work, e-mail me ( redxiii4@juno.com) and let me know; it took a while to finish this and I might have missed something.