Hello archer_root,
Fresh Durian: Fresh durian is available, I have purchased it even at supermarkets. I have seen it whole at Meidi-ya (way over priced). Try the department stores too. Takashimaya has the Hosokawa Fruit Store which has lots of high-end fruit (at high-end prices). It seems to me that I have only seen fresh durian in the summer here. Try the Travelt food court at Fujii Daimaru (near Shijo-Teramachi).
Figs: Figs are grown in Japan and are easily found in all grocery stores throughout the summer and autumn.
Obanzai: Kyoto’s favorite food!
Fresh Young Coconut: I have never purchased this but I am sure I have seen it at Meidi-ya, Travelt and so on.
Mango: Japan produces probably the most expensive mango in the world (I think from Miyazaki prefecture) and there are all the imported varieties available too. Recently, Japan is rather mango crazed! There is mango ’boutique’ chain that only sells mango. Mango are usually available at any supermarket.
If you are in Osaka or Kobe the Thai speciality grocery stores would be a good place to try too.
The wholesale markets have excellent selections of fruit as well and usually — at least in Kyoto — you don’t have to buy a truckload.