Cry me a river.
It's physically impossible! Let us estimate that one teardrop is a sphere (5 +/- 2) mm in diameter. This would make its volume to be (1.13 +/- 1.02) x 10
-6 m
3. Now, suppose we have a modest sized river (20 +/- 5) m wide, and (50 +/- 5) cm deep and (20 +/- 5) km long. The volume of the whole riverbed would then be (2.2 +/- 1.2) x 10
5 m
3. If I was to fill it up by crying, it would take me somewhere around 10^11 tears. Even if I were to cry 10 tears per second for 16 hours non stop every day, it would take me 475 years to fill it up. Since this is an order of magnitude longer than an average human life, I am afraid I cannot do it.