Very little angst at all:
Love 020 : for some reason, this didn't work for me (although I may give it another chance), perhaps because of the FL's seeming discomfort with anything physical, but it's a very sweet one about two gamers becoming a campus couple, and they're pretty much (refreshingly) devoid of drama.
Itazura Na Kiss : pretty sure everyone knows the premise to this, but, here goes: a silly, warmhearted girl is in infatuated love with a cold genius, they end up in a cohabitation situation, hijinks ensue. the 2013 version is really the cutest.
Sweet 18 : an arranged marriage between an 18 year-old and a prosecutor 10 years her senior. they go through little hiccups, and there are clingy second leads, but nothing particularly challenging. feelings are sparked considerably early, and once they're together, they're super adorable.
Has angst but remains fun/upbeat:
Heard It Through The Grapevine : the son of a prominent, wealthy family impregnates his poor (but incredibly intelligent) girlfriend, his conservative household is turned upside down. there are a lot of arguments because the younger generation rebels against the older generation (with very good reason), but everything is handled exquisitely., like a match of chess. this is really the only drama I can think of wherein the FL, if she tried, could control absolutely everyone, and that's so fun and refreshing to watch.
Glorious Day : it's a family drama, so there'll be the same angst that always persists (couples getting together or going through rough patches, mentions of illness, etc) but it's lovely & food for the soul. the single mother/author of three daughters gets conned & is left without a house, the eldest daughter wants to marry a man she finds unfitting & none of her girls besides her middle child (the FL) know of Mum's struggles: her solution is to move into the house her (unrelated) oppa lives in with his family (including two appropriately aged sons) for a short while while she attempts to mend their situation & talk her eldest out of marriage. the two families go from awkward acquaintances to....come on, this is a weekend drama, we all know the good ones dole out happiness generously. this one is guaranteed to make you feel warm.