Kure-nai has an ongoing plot but often wanders into slice-of-life territory especially in the middle of the series.
Other possibilities include:
Asatte no Houkou - supernatural premise, but pretty much fits your requirements nonetheless
Planetes - daily life among space trash collectors
Nodame Cantabile - daily life among aspiring classical musicians
Kemono no Souja Erin - lots of drama in some stretches, but also some quieter daily life sequences, particularly in the middle episodes
Seirei no Moribito - see
Erin; same author, too
Cross Game - daily life of high-school baseball players; some romance
Tokyo Magnitude 8.0 - while surviving an earthquake obviously doesn't constitute "daily life" per se, it still has slice-of-life features
Yomigaeru Sora - Rescue Wings - daily life of a helicopter rescue squad
Ghost Hound - another supernatural premise, but a lot of daily life, too
Two family comedies centered around clever animals,
Chi's Sweet Home and
Higepiyo, also fit your requirements, though the plot is less compelling than in some of the other shows above.