People with Parkinson Disease (or PD as it's also known) need special considerations as you correctly figured. However, keep in mind that most of those considerations are covered by special peripherals rather than specific UI. As a matter of fact, just following common WAI- ARIA guidelines is more than enough.
Keep in mind that, like many people with diseases, they want to forget they have a disease, and they don't want to be treated in a special way, so try to minimize any "hey, I know you have a very complex disease so I made a site for you" approach. Simple accessibility should be more than enough.
Since you need to do this, I assume you have access to people with PD, or at least knowledgeable professionals, so be sure to research the subject, because unlike what many UX professionals would think, working with people with diseases or disabilities is a really different thing that we might think. Additionally, you can read Improving Computer Interaction for People with Parkinson's Disease, a very interesting research on HCI for PD patients.
You can find a real case of the research for an app for PD patients at
If you have access to Springer, you can get these papers:
And on Google Books you can find Universal Access in Human-Computer Interaction: User and Context Diversity which I really recommend. I got it when we built a system for Alzheimer patients and its contents can be adapted to PD as well, so if it's within your possibilities, try to grab it. There are some free pages available just in case