The Dolphin is an animal which is sacred to Dionysus and Apollo. The reason for Dionysus' association with Dolphins stems from when he was at Naxos headed for Asia a group of pirates who planned to sell him into slavery. Dionysus caused ivy to grow all over the ship and he turned all the pirates (with the exception of the helmsman) into Dolphins. This act is when he started being worshipped as a god. This is the reason for Dolphins being important to Dionysius.
While Dolphins are the sacred animal of Dionysius, Eros is often shown riding on the back of one. This may be because his mother Aphrodite came from the sea and thus Eros may have had some affiliation with sea animals. It is however stated nowhere.