If the discussion is the majors, I just took a look on b-r.com, and in 1946 almost exactly one-third of players were in the Negro American League, and/or the Negro National League - not all the players were American but a lot. In 1932, the ratio appears to be even higher. In 1920, the first year that this kind of analysis can be done, it was still pretty high.
There are years that conform to what you have in mind, but it may be necessary to go back further than you expected.