Before you place them in the refrigerator, just untie the bundle of coriander leaves. Leave it for a while till the water on them(if any) gets dried off. Take a paper towel and spread the coriander leaves on it. Now roll it from one end to the other. Tie it in a plastic bag and store it in the refrigerator. Whenever you would need to use them, take out the ones towards the end of the roll. Remove the decayed leaves, if any, and then roll it back and place it in the refrigerator. The leaves would stay fresh for upto 1- 1 1/2 months.
Thanks to Lakshmi, my friend and neighbour for this great tip :).