Any non-combat mission rewards Diplomatic XP, every "Patrol X sector" mission includes at least one non-combat mission, and they also randomly occur in exploration sectors. Also, Starbase 39, K7, DS9, Bajor and Memory Alpha contain hidden DXP missions.
Most patrol missions has one noncombat mission, but some have two and others have none. Just click here and read each patrol mission to see if they have combat or not. There is the Rescue Deferi Captives which should give 10 DXP each day.
This sto diplomatic corps guide should help you out. Basically you have to do non-combat missions to get diplomatic experience and increase your diplomatic rank. It can be a bit of a grind but since you are at a low level you can alternate between non-combat missions and regular missions which will ease the grind.