Super romantic melodrama that wraps happily?

Just Between Lovers - highly recommend you this. It is basically all you look for. Very romantic scenes, very somber atmosphere, happy ending
Angel's Last Mission 
Nevertheless
One Spring Night
something in the Rain - this is not per say somber but it has really cute couple moments .

• Thirty But Seventeen (more light overall but deals with a lot of trauma/ptsd too)
• May I Help You  (Very underrated kdrama that deals realistically with death, the loss of loved ones, grief, trauma and how/what it takes to move on despite the supernatural bits. Very cute, mature romance as well. The leads communication with and support for each other is one of the best i have seen in a kdrama. )
• Angel's Last Mission: Love (Fantasy-ish. Very somber tone with some silliness in between, stellar acting of both leads but in particular of SHS. Huge Us Against Fate vibes)
  
• Tomorrow With You (Melo-romance mix up with a bit of sci fi mixed in. Super supportive, affectionate (married) leads of the strangers to spouse learning to live with and love each other kind)
  
• Chicago Typewriter (Love and friendship that endures and last lifetimes)
  
• Just Between Lovers  +1
  
• Link: Eat, Love, Kill  (Slice of life/thriller mix up with romance. Lots of trauma and its differing effects on people and their lives. Gets quite dark at times, but has also a bit of (black) humor mixed in)
  
• Find Me in Your Memory 
• If You Wish Upon Me  (takes place at a hospice, healing drama with a cute romance, somber to hopeful tones, quite sad tho)
  
• Doom at Your Service  (has a bit of humor, but tone is quite somber. FL is terminally ill, after all. Huge Us Against Fate Vibes)
• Come and Hug Me  +1