Do you have adobe image ready?
if so :
1 - open the image you want to use as an avatar in photoshop. Save it for the web. Name it 1
2 - create a new layer, draw eyelids (not totally closed) then save it for the web. Name it 2
3 - draw totally closed eyelids, save it for the web. Name it 3.
You should now have 3 different avatars : one with open eyes, another with not totally closed eyes and another with totally closed eyes.
4 - Open them in image ready, create a new file (same size as you want your avatar to be)
Drag and drop all the avatars on it (they'll appear on different layers).
There is a time control bar (with frames, etc) where you can choose to add a new frame.
5 - On this time control bar : create 3 new frames (you now should have 4)
In the first one, hide all the layers except the one where the eyes are wide open. In the second one, hide all except for the one with closed eyes. In the 3rd one, hide all the layers except the ones with nearly closed eyes and in the last one hide all except the one with open ones.
6 - Now you can set the time you want to assign to each frame : choose 5 seconds for the 1st one, 0 for the 2nd one, 0 for the 3rd one and 1 for the last one.
7 - Now you can save an optimised animated gif file :) IT'S DONE!!!
The image displayed shows how yours should look like if you've followed the steps.