Below is a list of Foods you can feed your Chocobo and a short explanation of how these
foods affect your steed.  All these Items can be purchased at the Auction House.

Azouph Greens - Obtained through Gardening
These greens Raise Affection for Chocobos undergoing a Mental Regime.
 
Carrot Paste - Obtained through Cooking
These pastes are generally given to young chocobos following a Physical Regime.
They slightly affect physical stats but as far as I can see, don't affect affection.
Vomp Carrot is an ingredient in this paste, so STR is an attribute that is affected.
 
Celerity Salad - Obtained through Cooking
It is believed these salads cure your Chocobos In-Love Status.  From the ingredients used to
synth this Salad, one can infer that it affects more than 1 stat simultaneously.
It alleviates many status abnormalities plus increases your Chocobo's energy.
 
Chocobo Blinker -
When equipped during a race, this item will slightly increase the stamina of a chocobo.
 
Chocobo Hood -
When equipped during a race, this item will slightly increase the receptivity of a chocobo.
 
Chocobo Taping -
When equipped during a race, this item will slightly increase the strength of a chocobo.
 
Chocolixir - Obtained through Alchemy
Using a Chocolixir allows you to replenish your Chocobos HP instantaneously during
Caretaking Cutscenes.  This in turns, allows you to take your Steed on additional walks,
races etc, increasing the odds of bettering your stats.
Is not affective on Chocobos that are already full.
 
Chocotonic - Obtained through Alchemy
Chocotonic wakes your Chocobo from a sleepened state.
 
Cupid Worm - Obtained through Gardening
When used, adds a huge affection bonus, but subsequently negatively affects Discernment and/or Strength.
 
Deluxe Carrot - ---
Deluxe Worm - ---
 
Fairweather Fetish -
Used during a race to temporarily clear up the weather.
 
Fire Biscuit - Obtained through Cooking
Used during a race to greatly reduce the stamina of an opponent chocobo.
 
Foulweather Fetish -
Used during a race to temporarily call upon a rainstorm.
 
Garidav Wildgrass - Obtained through Gardening
A Medicinal Green that cures Sickness [Stomach Aches].

Gausebit Wildgrass - Dropped off Mobs
A Medicinal Green that cures Injury.
Crane Fly (Level: 18 - 21) (Meriphataud Mountains)
Wadi Hare (Level: 11 - 14) (Dangruf Wadi)
 
Gregarious Worm - Obtained through Gardening
Restores Chocobo's energy.
 
Gysahl Bomb -
Used during a race to temporarily reduce the speed of all surrounding opponent chocobos.
 
Gysahl Greens - Obtained through Gardening, bought via Chocobo Vendor NPCs.
Satisfies your Chocobo's hunger while raising its affection.
 
Gysahl Slop - ---
 
Herb Paste - Obtained through Cooking
These pastes are generally given to young chocobos following a Mental Regime.
They slightly affect mental stats but as far as I can see, don't affect affection.
Tokopekko Wildgrass is an ingredient in this paste, therefore this paste does slightly
affect Discernment, and the medicinal properties of this wildgrass keep a young chick healthy.
 
Hi-Chocolixir - Obtained through Alchemy
Using a Chocolixir allows you to replenish your Chocobos HP instantaneously during
Caretaking Cutscenes.  This in turns, allows you to take your Steed on additional walks, races
etc, increasing the odds of bettering your stats.
A Hi-Chocolixir is quite a bit more potent than a Chocolixir, and will replenish more HP
immediately.  Is not affective on Chocobos that are already full.
 
Parasite Worm - Obtained through Gardening
I'm not positive about the affect of the Parasite Worm.  I believe it increases affection when
used and may remove a learnt ability as well.
 
Pepper Biscuit -
Used during a race to greatly reduce the speed of an opponent chocobo.
 
Shadow Apple - Obtained through Cooking
Used during a race to temporarily resist the effects of any detrimental items aimed at the chocobo.
 
Shadow Roll -
When equipped during a race, this item will slightly increase the discernment of a chocobo.
 
Sharug Greens - Obtained through Gardening
These greens Raise Affection for Chocobos undergoing a Physical Regime.
 
Speed Apple - Obtained through Cooking
Noticeably increase your Chocobo's speed during Chocobo Races.
 
Spore Bomb -
Used during a race to reduce the discernment of all surrounding opponent chocobos.
 
Stamina Apple - Obtained through Cooking
Used during a race to temporarily regenerate a chocobo's stamina.
 
Tokopekko Wildgrass - Obtained through Gardening
A Medicinal Green that cures Ilnesses [Colds] as well as slightly affects Discernment.
 
Tornado Salad -
HQ of Celerity Salad  [see: Above]
 
Vegetable Paste - Obtained through Cooking
These pastes are generally given to young chocobos following a Basic Care Regime, or
given to young chocobos with low affection that needs to be improved.
They do not affect physical or mental stats, but they do moderately affect affection.
Gysahl Green is an ingredient in this paste, therefore affection is directly affected.
 
Vomp Carrot - Obtained through Gardening
Vomp Carrots are given to Chocobos undergoing a Physical Regime.  They are most
commonly fed in combination with Sharug Greens, and directly affect your Chocobos Strength.
 
Worm Paste - Obtained through Cooking
These pastes are generally given to young chocobos needing a moderate to high affection
boost.  They somewhat affect Discernment and/or Strength negatively, while noticeably
boosting affection levels.
Cupid Worm is an ingredient in this paste, therefore affection is noticeably affected.
 
Zegham Carrot - Obtained through Gardening
Zegham Carrots are given to Chocobos undergoing a Mental Regime.  They are most
commonly fed in combination with Azouph Greens, and directly affect your Chocobos Discernment.