I own a rental. I rented it to a friend for the amount of space rent plus utilities and told her she is not to let anyone else stay there or the rent would have to go up. She has a boyfriend that stays over frequently and even has a key to the place. She has been there nearly 2 years and disregards anything I have asked her not to do. The agreement was all verbal. So, my question is can I legally charge her boyfriend rent for being there when I told her not to let anyone else stay there?

No, but you can have her evicted due to having another person staying there.

You need to draw up some sort of rental agreement with her and notate the no one else living there except you or it will cost an additional X dollars per month.

Sometimes friends are not the best tenants as they will definitely push the envelope with the friendship aspect.