Ichigo Marshmellow seems to fit the bill. Big sis taking care of her sister and friends. (Though sometimes the little sister seems more responsible, it's the big sis who's got a job.)
Less sure about this, but maybe
Kimi no Todoke. Ostensibly a romance, it's really the story of an outsider opening up. Very slow-paced, though. Great show and definitely produced a lot of smiles from me, though I'm not sure it's quite what you're looking for. (Check it out anyway.
)
And if you're up for something totally different that has that feel, I recommend
Shirokuma Café. It's about a polar bear who runs a café, and it's one of the most smile inducing shows I've ever seen.
Also maybe the often overlooked
Nekogami Yaoyorozu, which is about a lazy cat goddes who lives with an antique dealer(?been a while; I might misremember the job?). Includes lots of other fun deities, too.