Rainbow

Rainbow is a Hippocampus that was named by Tyson the Cyclops. He befriended Tyson and is bigger than most of his species, so he can carry him on his back without too much of a struggle.

The Sea of Monsters
Rainbow is half-horse, half-fish, or a Hippocampus ("Fish Ponies" as Tyson calls them). Rainbow appears with two other hippocampi at the beginning of the quest, as a gift from Percy's father, Poseidon. They take Tyson, Annabeth Chase, and Percy Jackson to the Princess Andromeda, Luke Castellan's ship. Rainbow is sad to leave his new friend, and performs backflips with Tyson on his back trying to get him to stay. When that doesn't work he follows them to the Sea of Monsters, and rescues Tyson from the ship CSS Birmingham when it explodes. He takes Tyson and searches the sea for Percy and Annabeth, finally finding them at Polyphemus' Island. Shortly after he rescues Percy and his companions, with the help of his fellow Hippocampi when Blackbeard's ship, Queen Anne's Revenge, sinks and takes them to Miami. After the quest Tyson rides him to the Cyclopes forges.

The Last Olympian
Rainbow is called near the East River when Percy is curious to know if Tyson is all right. When he learns about Tyson becoming a general, he asked if he would still give him apples to which Percy said yes. Percy asks Rainbow and his friends to carry them to Camp Half-Blood.

The Sea of Monsters
Rainbow will appear via use of CGI.

Trivia

 * Much like Percy has Blackjack, Hazel has Arion, and Jason has Tempest, Tyson has befriended an equestrian creature on a quest.
 * Rainbow is also the only equestrian creature met so far that is not scared or afraid of Tyson because of him being a cyclops.