Well, 3 ways:
1.) Master summon: beat emerald
2.) um... master summon again (but with much more painful process of mastering all summon materia. easier to just breed gold chocobo)
3.) um... well, have developed charas, and materias, and you should be fine... i think.

Yeah, so I have a question:
What do you have to do to reach chocobos with speed of 150+?

And about chocobo breeding: Well, it's painful and it's probably not worth it (since i beat emerald before gold chocobo and had KOTR). But, I think the racing is fun once you get to S rank. Yeah, I hate it when you have to sit in front of the TV watching your chocobo hop up and down 100 times before the other racers come.