The Dropbox API unfortunately doesn't offer a way to register an app or access token for access to a specific existing folder only, but I'll pass this along as a feature request. I can't promise if or when that might be implemented though.
The closest thing currently available is the "app folder" permission. That would limit any access tokens for your app to a special app folder created for your app; it can't be set to a pre-existing folder though, nor can the special app folder be made into a shared folder, or contain or be contained in a shared folder. For accounts using the English locale, the app's app folder gets created by default inside the "/Apps" folder.
