This truly was a hard one. There seemed to be a few with the word "Intimate," usually paired up with something like "Love" or "Confessions." Of course there had to be a few detective pulps that are shown below. I was hoping that I would find a title like INTIMATE DETECTIVE, but no such luck.
I CONFESS, Feb 25, 1927
ILLUSTRATED DETECTIVE, December 1931
INTERNATIONAL DETECTIVE July 1933
INTIMATE CONFESSIONS, September 1937
INDIAN STORIES, Summer 1950