I assume it's writing to somewhere in ~/Library/Application Support? The bad news is that's probably hardcoded into the app. I can think of some fairly dirty ways to fix it by loading an input manager and overriding NSSearchPathForDirectoriesInDomains to return a different path for this application, but that's probably a bit much.
If your external drive always mounts at the same point (normally /Volumes/<drive name>) then you could just create a symbolic link from the apps preferred place to the correct point on the external drive and it should just work.