Missing chocobo

[Niwashi]

I have the company chocobo mount

I also have the greens to feed the chocobo, but no mount.

These two statements contradict each other. Did you mean you have the mount, but not the ability to call it as a combat companion?

If so, then Manuel Bravo is right. You need to do the quest "My Feisty little Chocobo". You can pick it up from Docette at Camp Tranquil in the South Shroud. I don't think there is any GC rank requirement on that one, just that you need to have the chocobo mount, and be at least level 30.

EDIT:
Oh, and if you have access to a house or apartment (your own or from your FC) then follow up "My Feisty little Chocobo" with "Bird in Hand" to unlock the ability to train or customize your chocobo at your stable.