Believe me after a lot of thinking of today i did come up with this same solution and have already applied it :D
What i thought was that i can concatenate the initials of the departments to the course ids and course short names to all the courses and not just to the common courses ,this way the common courses for any departments will not create a conflict and each one will be treated uniquely.I think my university won't have any issues too as i'l mention in the user manual that teachers and students can search course ids in the format DeptShortName-CourseID .The fact that you gave me the same idea makes me feel i have thought in the right direction.
p.S:i have kept the course full names of common courses same..i hope that wont make any problems in identifying or searching courses for teachers and students in future?