This may take awhile, but trust me it's worth it! First, you need to buy all the stables at the Chocobo Ranch from Chocobo Billy. You then to aquire a Great & Good Chocobo, and then mate them using a Carob Nut which you steal from the Red Dragons on Bone Village. You should then have a River Crossing Chocobo or a Mountain Crossing Chocobo. Mate either one with the Good Chocobo and you should get a Blue or a Green. ok.. NOW that you have a Green and Blue Chocobo mate them together using a Carob Nut again and you should get a Black Chocobo. You then need to mate the Black Chocobo with the Wonderful Chocobo using a rare nut called a Zeio Nut which can be obtained by stealing them from the Goblins on Goblin Island, this may take awhile. Now when you mate the black and the wonderful if you dont get a gold chocobo keep resetting your game to that part until you then recieve A GOLDEN CHOCOBO!
To make them faster and better is to mate two "S" class chocobos it makes the offspring stronger in their stats. When you want to race them, but make them stronger just feed them every green you can at the Chocobo Ranch until it says "No Improvement", Which means you can't inprove on their skills no more!