Your best bet is to get some better lighting and turn off the flash... but...
http://graphicssoft.about.com/od/redeyeremoval/ss/peteye.htm
It's not perfect... but... it's slightly better. The one below is a little better...
http://www.thephotoforum.com/forum/photography-beginners-forum-photo-gallery/152986-dog-red-eye-blue-eye.html
Here is one I did using GIMP, which took about 2 seconds using only the burn tool, sized to the area of green, with about 7 clicks.
BEFORE
AFTER
Unfortunately the method I mentioned above didn't work on your picture of Chance... It has to do with the number of pixels in the area of question. In the picture of Oakley, there were about 50, where as in Chance's pic, there were only about 15, so there was less 'information' for the program to work with.
So I took the liberty with the paint brush and did this... hope it's satisfactory.