Is contacting this expert in the field something acceptable or would it be discourteous?
Yes, you can ask and you might get a reply, or not. If you demonstrate that you "have done your homework" and have some knowledge and not just interest then you will stand a better chance of success. What (or who) have you read? What have you explored? What ideas have you tried and failed with? 

You can certainly state that you are looking for a research problem suitable for a dissertation and that you are coming up short. You can ask for guidance on where to search (additional papers to be read, people to contact...). 

However, it is unlikely that a problem will be dropped in your lap. If you were able to attend a seminar with the author's group you might be able to do better. And be aware that a "problem" quickly thrown out may not be suitable as it may end up trivial or impossible. Such things are often approached only gradually. 

But it isn't discourteous to ask as long as you can show that your search isn't just a random one. 

But in general, also be prepared to work on a few problems before you come up with the one that leads to success. Even an unsuccessful attempt can teach you how to be more successful with the next one.