You can use some chicken wire or something else like it to surround the sunflower. You may need to tie the wire together to make it go around the flow...
This is an instructable to help protect sunflowers from critters.
Step 1: Cover the plant
First you should cover the sunflower when it is small with the top of a soda bottle. Make sure to take the label off the bottle and take the cap off. Then push the bottle in the ground around the sunflower if that does not work you could mound up dirt around it. You should water the flower because it won't get much water from rain with the small hole. Make sure it is in tight so animals can't knock it over. Take the bottle off when the sunflower is too big for the bottle. These are some pictures of the soda bottle. One is when it is whole one is cut and one is on the ground. I did not have a sunflower so I just put it on the ground.