There's a bit of homelessness in
Kodocha. One of the characters used to be homeless until Sana found him and took him home and made him her manager. And the whole family eventually loses their home. Although they don't exactly live on the street.
The protagonist of
Fruits Basket is homeless and living in a tent in the beginning of the series.
There's homeless people in
Paranoia Agent (also from the director of Tokyo Godfathers, Satoshi Kon), although the show is not particularly happy. It's a suspense/thriller/psychological mystery show.
Ie Naki Ko (aka. Nobody's Boy - Remi) and its 1996 remake
Ie Naki Ko Remi feature a boy, and in the remake a girl, end up homeless and traveling Europe. I've not watched it, but from what I gather, it has many sad moments.
The main characters of
Grave of the Fireflies end up homeless after their hometown is bombed in World War II by the US. If you didn't already know, this movie is
sad. There are some happy moments, though.
And then there's
Mr. Stain on Junk Alley, which is just plain
weird.