You absolutely can! I have a Zojirushi fuzzy logic rice cooker, and I use it all the time to cook beans. It works amazingly well!
I don't know what size rice cooker you have. I own a 5-cup size, and this is the recipe i use:
Soak 1/2 lb (1 cup) of dried beans in plenty of water for at least 8 hours or overnight.
Drain and rinse the beans, and place in the rice cooker bowl.
1/2 medium onion, finely chopped
2 cloves of garlic, minced
1 Tbsp olive oil
very hot or boiling water to cover beans by 3 inches
Set rice cooker to "regular cycle" and let the rice cooker do its thing! It will switch to "keep warm." Add 1 tsp salt when done cooking, and let the beans absorb the salt for a bit before serving.
When cooking black beans and pinto beans (my two regulars) the beans are done perfectly after one cycle of the rice cooker. However, some beans may take longer, and some rice cookers might behave differently. My cookbook recommends setting a timer. Once you figure out how your own rice cooker works you may not have to.
I really recommend The Ultimate Rice Cooker Cookbook, by Beth Hensperger and Julie Kaufmann. It has tons of great ideas for using both fuzzy logic and on/off rice cookers for many, many foods and recipes.