Here is the guide to Chocobo Breeding.
First you need to buy all six stalls at the ranch. Next you need to fly to the Chocobo tracks near the Gold Saucer to catch two Good Chocobos. A male and a female. Once you have done this, fly down to Mideel and catch two great Chocobos. A male and a female.
Then fly around the mountains on the Northern continent until you find a house with a small patch of grass by it. Go in a talk to the green Chocobo to get an Enemy Skill materia. Then buy one Sylkis Green from the sage and use W-Item to get it up to 99(While you are at the Sage's house, run on the grass untill you incounter a red dragon-like monster. You need to steal two Carob Nuts from these monsters.). Feed each of your new Chocobos 85. Then go race them all up to class A. (This increases your chances of getting what you need.) Then mate(SAVE FIRST!!!) one of the good Chocobos, with one of the greats. Use a Carob nut and you should get either a green or blue Chocobo. Then mate the other two and keep resetting untill you get the opposite, that is the opposite gender.
Feed each of these 98 Sylkis Greens and race these up to class A, too. Ride the green one out of the ranch and take it in the Airship. Fly over to the Wutai continent and ride the Chocobo down to the southern tip. Go inside the cave to get the Mime materia. Take it back and get your Blue Chocobo. Take it to the Mideel area and ride it East to the next materia cave. (I forgot what was in this one.) Take it back and go do some stuff, the boy won't let you mate them yet. You need to release all of your normal Chocobos. Go get a couple more Carob nuts, you'll need them, too. I usually save Yuffie's sub-quest for now. You can also get your people their ultimate weapons and fourth limit breaks now.
Save your game and mate the green and blue, once you have the chance. Use another Carob nut. You should get the black Chocobo. Go out to the Northern continent and run along those tracks to catch a wonderfull Chocobo of opposite gender of your black Chocobo. Feed each of these Chocobos 98 Sylkis Greens and race them up to class S. (And I know how to always beat Joe. Email me at dragongirl05@ hotmail.com and I'll tell you.) Fly to the northeastern islands and run around in the woods and steal a Zeio nut from the Goblins. You can also learn enemy skill, Goblin Punch from them. Ride your black Chocobo over to the cave by Corel and ride to the cave in the desert nearby to get HP MP Switch materia.
Once you can mate the Black and Wonderfull Chocobos, save your game and breed them untill you get your Gold Chocobo. Feed it 98 Sylkis Greens if you want go and kick some serious butt at the races. Take your gold Chocobo up to the Goblin Islands and ride up to corner of the map to find Round Island. In this cave is the ultimate summon materia, Knights of Round!!