If you are arriving/departing FUK and going to Nagasaki on Saturday, what you should consider is the
Northern Kyushu Rail Pass. A day trip to Nagasaki alone costs less with a 3-day Northern Kyushu Rail Pass (7,200 yen) than the normal return fare plus the limited express charge. A 3-day pass should also take you from Hakata to Hita on Sunday and Aso to Kumamoto and even back to Hakata on Monday. A real bargain. @:-)
Anyone staying overnight in Kumamoto on Monday and returning to Hakata on Tuesday should get a 5-day pass at 9,260 yen if they are also going to Nagasaki.
Unlike the Japan Rail Pass, the Northern Kyushu Rail Pass may be bought after you arrive in Japan at Hakata Station or TISCO Travel Information Center located on the first floor of the International Terminal of Fukuoka Airport. When you purchase a pass or exchange a voucher (which you have bought outside Japan) you can specify the date when the pass should be activated and reserve seats (free of charge) as well. If you arrive in Fukuoka on 2nd, you can buy a pass on arrival to be activated on 4th for a trip to Nagasaki.
Seat reservation to/from Nagasaki is optional. The train we plan to catch has 2.5 cars with reserved seats and 3 cars with unreserved seats. If you are reserving seats the trains we plan to travel on are:
Kamome #7 : dep. Hakata 07.54 - arr. Nagasaki 09.50
Kamome #38 : dep. Nagasaki 17.20 - arr. Hakata 19.14
If you have difficulty getting reserved seats for the Nagasaki trip what you should tell/show at the
Midori no Madoguchi is that you want a reserved seat or a Shitei-seki (指定席) on April 4th (4月4日) on the following trains.
かもめ7号 博多発 07.54 長崎着 09.50
かもめ38号 長崎発 17.20 博多着 19.14
If anyone is still in Fukuoka on Sunday and not going on the onsen trip, they can hop on the Kyushu Shinkansen for a 33 min ride to Kumamoto to see the castle and cherry blossoms. If you can stay until the evening you might be able to catch the last day of floodlighting of the castle during the cherry blossom season. The normal return fare between Hakata and Kumamoto on the Shinkansen is 9,220 yen!