Try looking for Casio G-shock shops, as to my knowledge, some of the G-shock models used the CR2320 battery. (Especially the DW-5600C-1, DW-5600C-1V, DW-5600C-9V, DW-5600C-9CV and DW-5800C-1V, the first G-shock with Bezel protector)
BTW, your Kirium is Swiss made right? Reason is, if swiss made, try to get the Renata brand of battery (from Europe), otherwise a Maxell or Sony battery for the Asian version. (Note: depends on the watch movement/engine)
Lastly, if indeed the CR2320 is no more in production or very difficult to find, try to use the CR2016 battery instead of the original CR2320 one. I was told some people had been using them for years in place of the CR2320, when they could not get the CR2320, and have not had a problem. But first, please check with the watch repairer if the CR2016 can be compatibale in the Kirium or not.
As a last resort, you can order online.
(I was told Tag Kirium F1 sold in Europe used the 394 battery - not sure if the same as your CR2320)
Cheers.