You can get to COEX easily using the subway.
Select your origin and it will tell you how to get to COEX.

From Gangnam Express Bus Terminal      From Nambu Terminal
From East Seoul Bus Terminal    From Gangbuk (center of Seoul) area

From East Seoul Bus Terminal
Take the Subway Line #2 in the direction towards Gyodae (Seoul National University of Education), and get off at Samsung station. Use the Exit No.5 or 6 connected to the COEX Mall.