I never had a problem as a white man myself in Japan, and my 2 daughters who are 50/50 never had a problem either.
When I was still working for African French speaking countries in Japan I had contact with several black men with Japanese wife, there are also some black US-military people who prefer later on to stay in Japan after retirement.
However the number of black people in Japan remains to be very small, why should a black man from Africa or elsewhere from far away prefer Japan as his or her permanent country?
About Koreans in Japan this is a totally different matter, there are 3 groups of Koreans in Japan.
1 - the North Korean group,
2 - the South Korean group,
3 - the Koreans, who prefer to become Japanese citizens and disappear to be Koreans.
About group 1 - these people have problems everywhere in Japan, if you promote North Korean politics/propaganda and refuse to let your children go to Japanese schools, are keeping control over gambling spots and similar legal grey zones, you are clearly not welcome.
About group 2 - South Koreans are doing very well in Japan, but they prefer to keep South Korean nationality, most of them are located in certain places only, like trading spots in Fukuoka and Osaka and they are not known to be interested into dating Japanese men or women either.
About group 3 - Koreans, who said good-bye to Korea, took over Japanese nationality and Japanese names. If you don't know them personally, you will have no idea that he or she is originally from Korea. These people are very successful in restaurant business, entertainment business, and if you look any TV-show in Japan, you can be sure, some of them are originally from Korea.
I am 60+ and so I can comment only about 'stars' of my time when I was still younger. For example Wada Akiko、Go Hiroshi, Rumiko Kuroyanagi, are Koreans, and believe me they get plenty of fan-mail from Japanese people.
(=Kim Bok-Ja) Can you tell me how she is 'discriminated'?
About group 2: If you visit places in Tokyo like Takadanobaba near Shinjuku or Akasaka near Hie Shrine, you will notice the large number of restaurants/otherwise entertainment businesses which belongs to the South Korean community using their Korean names only - if the Japanese do not like Koreans, I wonder why these places are full with Japanese customers every evening.
If you think, Koreans have problems with dating in Japan, you might check first if Japanese have problems with dating in Korea.
While Japanese and Koreans are looking very similar, they are clearly different in their way of behavior, food etc. - they do not have so much in common as you might believe.
Young men from both countries, South Korea and Japan and Taiwan too, are known to have 'dating problems' and often are looking for a foreign wife from other Asian countries, so it seems they are not so much discriminating.
As a fact, some people do well and others do not.
Well known in South Korea and Japan is the life of 'Rise', a Korean girl born in Japan, died in South Korea, funeral in Korea and grave in Japan.