It depends on the context. If the sentence refers to the type of language she uses then coarse refers to using rude and offensive language and you could use 'vulgar', 'crude', 'uncouth'. If the sentence refers to the quality of her voice then coarse can mean rough and unpleasant to listen to and you could use 'harsh' or 'rough.'

Perhaps you mean that her voice was rough or that she was uneducated?

"coarse" is a very good word to describe this kind of voice.

Yes there was such common,harsh,uncouth,vulgar cowboy...