There are Five different colored Chocobos, here are what they are, and what they can do:
Here are instructions on how to raise a Blue or Green Chocobo:
To get a Mountain or River Chocobo, you need to breed either a Great Chocobo with another Great Chocobo or a Good Chocobo with a Great Chocobo. The higher their class is, the better chance you'll get a special Chocobo (raise their class in Gold Saucer Chocobo racing). Also, you need to use a Carob Nut, which you can steal from a red dragon that you sometimes fight in the grassy area just below Bone Village. It's possible to get a Mountain, River, or gold Chocobo. This is what they look like, Green is Mountain, and Blue is river:
These Next instructions tell how to get a Black Chocobo:
You get a Black Chocobo by breeding the Mountain Chocobo and the River Chocobo together with a Carob Nut. Once again, a higher racing class for both Chocobos will increase your chances of getting the Chocobo you want. The Mountain-River Chocobo is quite useful, although wouldn't it be nice to have a Chocobo that could cross the ocean? Here's what the Mountain-River Chocobo looks like:
These Next Instructions tell you how to get a gold Chocobo. NOTE: A gold Chocobo is NEEDED to get K.O.T.R. "Knights of the Round" Summon Materia.
1. Your first step in getting the Gold Chocobo is simply getting the right kind of regular chocobo. The Chocobos you need are Great Chocobos and Good Chocobos. I found mine by the town of Mideel (where Cloud ends up during the 2nd CD).
2. When you get a male and female of each you need to get a Carob Nut. These nuts are easy to find, they are located in the grassy area by Bone Village (where you follow Aeris to the Lost City). You should encounter a weird red dragon thing, well anyways steal from him until you get the Carob Nut (you should get at least 2 before leaving).
3. Now go to the Chocobo stables but SAVE before entering it makes this a lot easier. Now you need to mate the two Great Chocobos until you get either a green one or a blue one (that's where saving comes in handy). Then do the same with the two Good chocobos until you get the other color that you don't have yet.
4. Now you should gain levels since your new Chocobos aren't old enough to be mated. While you are doing this go get another Carob Nut. Check back to the stables every 10 battles or so until you can mate the two colored ones.
5. Now that you can mate the new chocobos SAVE the game then enter the stables. Now mate the two new Chocobos with the Carob Nut until you get a Black Chocobo.
6. After you have done that you can let every Chocobo back into the wild except for the Black one. Now go find a Wonderful Chocobo located in some tracks in the east end of the snowy area. It is hard to find but hope that it is the opposite sex of the Black Chocobo.
7. If you have gotten this far it isn't over yet. Now go as far to the West as you can and search in the ocean for some uncharted islands. One of them will have a forest in it and be called Goblin Island. Go into the forest and steal a Zeio Nut from them.
8. Now for the time consuming part. Go to the Gold Saucer and race the Black and Wonderful chocobo until they are in the S rank (this increases your chances of getting the Gold Chocobo.
9. After both Chocobos are in S rank go back to the stables and SAVE. Now mate the Black Chocobo with the Wonderful Chocobo using the Zeio Nut until you get the Gold Chocobo!
10. Congratulations now you can get the Knights of the Round summon materia on an uncharted island in the North West of the map!
Here is what the infamous gold Chocobo looks like: