The Isle of Reincarnation is a legendary place said to be the home of several legendary monsters, including Phoenixes. So far, My Monster Rancher is the only game that allows this as an exploration location, and only at certain times of the year.

This is quite possibly the island that Niton recounts to the Searchers during his fictitious account of how he retrieved the Phoenix mystery disc. The disc (and the story) turn out to be fake, but the fact that it is a beautiful island that includes a volcano may mean that it's the same one.