A Gentleman's Dignity would probably be the funniest. 

The bulk of the series itself isn't overly focused on comedy, but at the start of each episode there are short comedy skits usually based on the protagonists adolescence, they are hilarious af. 

Chief Kim is a close second. 
Reply 1988
Reply 1997
Age of Youth
You who cane from the.stars. Master's sun. Marriage not dating
Age of Youth! both seasons!!

Chief Kim

Beautiful Gong Shim

(Namgoong Min rocks my world)

The Ex-girlfriend club


Never laughed so much then watching this one