As far as I know, importing is not a big issue for these species. It's rather a problem with exporting from the country of origin.Is there any possibility that Japan as a major marine and acquatic mammal exhibitor (at various, if not quite a few collections) may be able to import any dugong or African manatee?
For dugongs, there is still a small population left in southern Japan, so a rescued individual from there will be the highest chance.
For manatees, it will be possible if some overseas facility offers captive individuals.