The No. 1 Ladies' Detective Agency
If cozy means little to no violence, this is it.
If it means no complicated plot, ditto.
EDITED: Not quite as non-violent, but perhaps in the direction you are asking for, and easy to try out, is
The Moonstone:
http://en.wikipedia.org/wiki/The_Moonstone
http://www.gutenberg.org/ebooks/155