for a heartwarming drama... try candy house, perhaps? it may be more contemplative & raw about life than heartwarming tho... it made me cry, smile, & laugh. idk, when I think of something that's heartwarming I think of happiness & puppies, lol. I also recommend family's form, & you might also want to check out the jdrama hope because if it follows the kdrama then it must be uplifting/heartwarming.
I don't watch/haven't seen too many live-action manga adaptations, but I think koe koi & nodame cantabile are pretty good. I have soft spot for hana yori dango, too. if that's up your alley I suggest checking it out. oh, & nigeru wa haji da ga yaku ni tatsu, which has the scriptwriter from juhan shuttai.
others, not from manga or entirely fit the heartwarming bill but I just wanna toss the names in here: love shuffle & q10.