I think this should work with a simple notification. We use the following Code in the SyncAdapter of Mirakel to do so:
mNB = new NotificationCompat.Builder(this.mContext) .setContentTitle( "Mirakel: " + this.mContext.getText(R.string.finish_sync)) .setContentText(last_message) .setSmallIcon(android.R.drawable.stat_notify_sync) .setPriority(NotificationCompat.PRIORITY_LOW) .setContentIntent(p); this.mNotificationManager.notify(this.notifyID, mNB.build());This should be fairly simple to modify for DAVDroid