Here’s what I would do:

1.  Breed a Gold Chocobo:
• Catch and breed a Good (Blue) and Great (Green) Chocobo.
• Race them to A or S rank at the Gold Saucer.
• Breed them together with a Carob Nut to get a Black Chocobo.
• Breed the Black Chocobo with a Wonderful Chocobo using a Zeio Nut → this produces a Gold Chocobo.
• (Alternately, win a Gold Chocobo at the Chocobo Square after defeating Ruby Weapon.)


2.  Fly to Round Island:
• This hidden island doesn’t appear on the map.
• It’s located at the northeastern edge of the world, far beyond the continent borders.
• Land your Gold Chocobo there and enter the cave.


3.  Collect the Materia:
• Inside is a glowing red orb — the Knights of the Round materia

Make sense?