Itinerary for 4 days/3 nights in Kyushu?

I am planning a 4 days/3 nights itinerary in Kyushu, but I am having some problems. The places I would like to visit are Fukuoka, Nagasaki, Kumamoto and the Kawachi Fujien Garden (I will be there around the May 10th). Which order should I follow to visit this places? I will arrive to Hakata from Osaka around 11-12 a.m. The garden can be visited the last day or the first, in the way to/from Osaka...

If this is the only problem you have, that's pretty good. :p There is really no correct order, any combination is fine. (If you visit Fukuoka between Nagasaki and Kumamoto you might just lose about 40 minutes of travel time since if you go directly between Kumamoto and Nagasaki you can transfer at Shin-Tosu instead of going all the way to Hakata.)

It seems like your itinerary is pretty decided already right?
If you arrive at Hakata then I would suggest spending your first day at the garden, 2nd day in Fukuoka, then travelling to Nagasaki and Kumamoto on the 3rd and 4th days, before returning by Shinkansen from Kumamoto. As Firas said in their post though, whether you travel to Kumamoto or Nagasaki first doesn't really matter. The only thing that might change it is if there are particular events or sights that are only open on one of the two days, or if there is a specific hotel you want to stay at that only has rooms for one of the nights, so you should just check that before you decide.

Thank you guys! :) What do you think about this itinerary?
Day 1: Osaka - Kawachi Fujien - Hakata (stay in Hakata)
Day 2: Hakata - Nagasaki (stay in Nagasaki)
Day 3: Nagasaki - Kumamoto - Hakata (stay in Hakata)
Day 4: Half day in Hakata and train to Osaka.
Do you think the time I am thinking to use for each place is not enough? In Kumamoto I want just to visit the castle and the Suizenji Garden.