I'm not sure how you could do that with Automator alone, but if you combine it with iCal, it isn't hard. Here's what to do:
1. Open Automator and choose the Application template for your new project.
2. Use the search box to find the Quit Application action. Add it to your project and select the application you want to quit from the pop-up menu.
3. Save the project wherever you want—just remember where—and quit Automator.
4. Open up iCal and double-click on the day you want to close the application (or the day you want to begin closing it if you plan on repeating it).
5. In the New Event pop-up, choose when you want the application to close for the from option and whether and how often you want it to repeat.
6. For the alarm option, choose Open File. This will add a few more options. Click the next alarm option and choose Other… and navigate to the file you created in Automator. Finally, choose how many minutes before or after the from date you want the application to quit.
7. Configure anything else you want here and then click done. When the time you choose rolls around, it should quit the application for you.