Nils Asther (The Bitter Tea Of General Yen)
Charles Laughton (The Old Dark House, Island Of Lost Souls and The Private Life Of Henry VIII)
Paul Muni (I Am A Fugitive From A Chain Gang)
Claude Rains (The Invisible Man)
Paul Robeson (The Emperor Jones)
Note: I've had trouble figuring out whether Charles Laughton belongs in drama or comedy—I had initially nominated him in the category of drama for his performance in The Private Life Of Henry VIII, but as Erik Beck of the Boston Becks pointed out, it's really a comedic performance (though it does, I think, have dramatic elements). I tried him out for a while in comedy, but then I took a second look at two more of his performances from 1932-33—The Old Dark House and Island Of Lost Souls—decided they were also nomination worthy, added them to list of credits and found that overall, he had tilted back into the category of drama.
Of course, the other solution would be to nominate him in both categories, in comedy for Henry VIII and in drama for the two horror classics, but I prefer to limit actors to one or the other in any given year. Leaves more slots for other actors and lets me spread the wealth. You're free to approach the question differently.
