How to best keep a bunch of coriander fresh?
For almost all delicate green herbs, the best thing to do is 


Hold them by the bottom of the bunch and gently swirl in plenty of
cool water to remove all the dirt
Gently shake to remove excess water
Wrap loosely in a damp paper towel
Place in a plastic bag and store in the crisper drawer of your refrigerator


This will keep most herbs fresh for many days.