I agree that using absolute paths may not be the way to go but to solve your problem you could get the name of the user like so
String username = System.getProperty("user.name");
From there you can use the windows file structure to get to the documents folder
String documentsFolder = "C:/Users/"+username+"/Documents";
With that directory path you can read and write to that folder. This folder structure would only apply to windows and would need to be changed for Mac or Linux machines, but the username can be obtained the same way.
Just a suggestion. If you are supporting windows machines only maybe you can create a registry with the start and end date of the application and use that as a reference point which will be consistent even if the application is uninstalled or re-installed. Also maybe creating a System variable with the date could be another way to go. Just a few thoughts.
Hope this helps