1 Litre of Tears, based on the diaries and life of a young woman with a progressive incurable degenerative disease. It balances happy and sad well, so it's not 11 hours of tears. But when they do come.... Not sure if I'll be able to watch it again but I'm glad I did.
This was asked in the Japan section, but if you're open to other things, may I suggest He's Coming to Me? It's mostly fun, and so full of kindness and warmth it brings many smiles. But it's about a ghost and a young man who can see him, and that brings complications. Don't want to say too much but there was a moment when I couldn't continue and had to pause, blow my nose, sob, sob again, and pull myself together enough to go on. Sound promising for you? :)
These sorts of mixes between happy and sad are more powerful for me. Both of these also include supportive family and friends, and that always makes it easier for me to cry hard. Good luck finding what you need.