The miracle solution for long-term cilantro storage is this:
1) cut the stems
2) fill a tall container with 1-2 inches of water
3) stand the cilantro up
4) put the whole thing in a large sized flexible plastic bag (no holes)
5) blow it up (not with explosives); blow it up with air from your lungs. This adds CO2. Cilantro **needs** it.
6) Store the contraption in the refrigerator, away from the freezer compartment.
Cilantro will last for one month or more!
My best recommendation for green onions and just about all other fresh vegetables is to invest in airtight containers. What you do is line the bottom with two layers of paper towels, wash all items and just shake them off (you want a little liquid). Place them in the container loosely so air can circulate. Leave both vents open. AMAZING RESULTS! One or more months for most items; including: lettuce, green onions, red/green peppers, carrots, radishes, cabbage, parsley.
I've found that two things are very important: 1) an airtight seal and 2) the vents that provide what seems to be the exact right amount of air.
Hope this helps!