Well, here's what I did for my black Chocobo, maybe someone can figure it out.
Egg: Bought it from the NPC in Ru'Lude Gardens, the most expensive one he had.
Raised it in Bastok Stables, started on Sunday at 12:30am EST roughly going into Monday morning
All I ever feed it was either Gyshal Greens or Gausebit Grass when it got sick.
Everyday I took it for walks, then fed it twice for the day, my plan was always basic care except for once, when it was sick I set it to rest for one day. I would watch over it maybe once every 5 days.
In all the walks it had in childhood, it only met the Chocobo Blood being raised by the Galka.
By the time it became a teen it had the black tips, so I doubt anything you do then could change it.
My chocobo has a normal tempermant, and can get along easily with anyone.
That's it, thats all I could remember from it's childhood, I honestly think it just random, and only through breeding you'll be able to get the color you want 100%.