When I first learnt to cook and handle the kitchen, I had to keep throwing out the cilantro before I could finish consuming it. It would almost always turn brown in a couple of days! Let me tell you the methods I have previously used to preserve it. I have washed it then dried it carefully and air-dried it as well then laid it in a ziplock bag and frozen it; I have removed the leaves and put in an air-tight box with paper tissue wrapped around it (tried it washed and unwashed); wrapped the whole bunch in newspaper like a burrito. None of these worked. Then I started using the method below.
Fill a jar or a water glass enough to cover the roots. The mouth of the jar should enable the stems to stand upright and not wilt down due to extra space, then cover the cilantro loosely with a plastic bag and tie a knot at the mouth to hold the bag in place. Then it is ready to be stored in the refrigerator which will last upto 10 days. Change the water every 2-3 days.
Before you place it in the jar, wash it and lay it down to dry over a towel. It doesn’t take too long to dry around an hour left out, depending on the humidity level on that day. Then make it stand upright in the jar. When you do need it, it is washed and all ready to use. It smells fresh and it is crisp when you are chopping it. Give it a try!