First off, when my dog is sick I use Baby Rice. It dissolves easily in water or broth. You don't have to cook it and you can make it the consistency that you want. I always keep a box handy if my dog gets sick I don't have to worry about cooking anything. I also keep a box of low sodium chicken broth on hand as that always makes it more palatable.
I have done rice in the slow cooker for myself. It comes out beautifully. Again, I use chicken broth as the liquid and it takes about 2-3 hours on high. The time will depend a lot on your cooker. Here is where I found out how to do it:
http://crockpot365.blogspot.com/2008...t-as-rice.html
I also use the slow cooker for chicken. Usually, I just put a whole chicken in. You don't need any liquid. It will make its own broth. When it is done, I just dispose of the skin and bones, skim the fat off the broth, and go from there.