With poser you never know, of course, but it shouldn't be that difficult. This is how I would try to tackle this:
1 - apply all morphs to get the crying face.
2 - spawn a prop of the head of the character you want to use and set the original head to be it's parent. With a magnet push everything above the eyes inward.
3 - apply a 'water' or 'glass'  texture to the face prop (with IOR), and open a displacement channel.
4 - in the displacement channel use an 'add' node with negative value (say -0.1) in the second input to ensure the 'water' surface is below the skin.
5 - In the first input add either
 - an image map with a black base and in the position of the eye corner a white spot and a gray smear up. Create a frame node and build a branch to connect this with the v-offset input of the image node in a way to make the v-offset increase (or decrease? I always forget poser's convention here) as frame number rises.  Tune height, scale and add modifiers to fit. Add a sine or cosine to the u-offset input to make a realistic 'trickle'. 

• if you're  math wizard create a spatial function in the (u, v, frame#) domain to do same.  A combination of a paraboloid for u and a trochoid for v, truncated in v,  will bring you a long way. 

Not tested, no guarantee.