The series never had more than three actors billed in the main titles, but Doohan, Whitney, Takei, and Koenig were all signed to multi-episode contracts which were renewed (or cancelled, in Whitney's case) every thirteen episodes. That makes them regulars in my book -- just not main characters.
(I believe Koenig began as a day player and was upgraded to a regular; as far as I know Nichols and Barrett were always paid as day players.)
Of course, in practice, all of the supporting actors I have listed were "regulars" and are listed as such in
The Making of Star Trek.