First of all we’re going to tell you where you can find the different chocobos, then we will tell you what to do.
Chocobo Ranch: Poor/weak
You will need to gain a lot of money. You can do this by winning lots of battles, or master an “All” Materia then sell it. That could take some time though.
Buy all the stalls in the ranch place.
Get a blue Chocobo by mating 2 good or great chocobos and giving them a Carob Nut. I also suggest racing them until A class or better. To obtain Carob Nuts you can buy them from the wonder square for 500 gp or by stealing them from the Vlakarados near bone village.
Get a green Chocobo the same way. If you got a green one the first time then obviously you are going to try and get a blue one now. Make sure and save right before you breed the 2 chocobos just in case you don’t get what you want.
Rocket Town: Mediocre
Icicle Inn: Wonderful/weak Mideel: Great/fair
Now that you know the locations of the different ranks of the chocobos we are now going to tell you what you need to do to obtain them.
Now hopefully one is a male and the other a female. If not then just turn the game off and “rebreed” the 2. If you did, then breed the green and blue Chocobos together, while using a Carob Nut to get you a black Chocobo.
Go to the tracks around the Icicle Inn area and catch yourself a wonderful Chocobo. Next you need to get a Zeio Nut on goblin island which is lovated on the easter part of the map from the sky it looks like the head of a Chocobo. You can steal them from the goblins on that island.
Now race the black Chocobo and the wonderful Chocobo until A class again, and now you are ready to breed the Wonderful with the black one that you should have with the wonderful while using a Zeio nut. Remember to save right before breeding again. And now you should have a gold Chocobo and can go anywhere on the map now.