Umisachi-Yamasachi (海幸山幸) is limited express train that is operated between Miyazaki (宮崎) and Nango (南郷). This train is named from Yamasachihiko (山幸彦) and Umisachihiko (海幸彦) in Japanese mythology.
This is not a real express train and is a kind of cruising train for sightseeing along Nichinan line (日南線). This train is suitable for the tourists who go to Aoshima (青島) and Udo Jingu shrine (鵜戸神宮) at Nichinan coastline (日南海岸). This train makes your trip more memorable.
If you use Japan Rail Pass, you can take this train with no extra cost. I will show you some images of this train and tell you the details.
This itinerary includes all part of Kyushu and covers many popular spots in Kyushu island in 7 days. So you can simply use Japan Rail Pass 7 days. You may start this itinerary either from Tokyo or from Osaka. But if you can start this from Tokyo, you need to skip Sasebo and Saikai National Park because of the time. And also you need to take the overnight train Sunrise Seto/Izumo if you start this from Tokyo on 7th day. Otherwise you cannot complete this itinerary. As long as you catch “Nobi Nobi seat” on Sunrise Seto or Izumo before the date change, you can continue to travel without any extra charge. (Please refer Japan Rail Pass official site, “Notes regarding use” point 6.)
Kirishima (きりしま) connects Miyazaki (宮崎) with Kagoshima-Chuo (鹿児島中央). This train is an intercity train and stop at lots of regional cities in Miyazaki and Kagoshima prefectures. If you travel along the southeast coast of Kyushu, you may need to take this train. Especially when you go to Kirishima mountains, you can take this train to Kirishima-Jingu (霧島神宮). And then transfer to the local bus.
Nichirin (にちりん) connects Beppu (別府) and Oita (大分) with Miyazaki (宮崎) and Miyazaki airport (宮崎空港). A few of Nichirin are extended to operate to Nakatsu (中津) and even Hakata (博多). Hyuga (ひゅうが) is an intercity train in Miyazaki prefecture. This train is operated on same route as Nichirin. But it is operated between Nobeoka (延岡) and Miyazaki airport. If you travel along the east coast of Kyushu, you may need to take these trains.