Coleby was born in Sydney, and is the son of actor Robert Coleby and brother of Actress Anja Coleby. He attended the Mona vale Film and Television school at the age of 6 where his passion for screen acting began. It was not long after leaving the Mona Vale school that Conrad performed in his first professional role in the mini series "Tanamera - Lion of Singapore" in 1989. After continuing to study drama at Somerset College on the Gold Coast, finishing school in 1996 with a full "Blue" honours in dramatic art, Conrad decided to carry on his study at the tertiary level completing a Bachelor of Arts in Dramatic Arts (Acting) at the Queensland University of Technology in Brisbane mentored by Leonard Menach. In his third year in 2000, Conrad traveled to Singapore, Los Angeles, New York and Stratford on Avon performing the title role of "Lewis" in Louis Nowra's Cosi as part of the university's first ever world tour.