@RoarDa: I think this can be done for individual contacts by following the steps below:
Open the Contacts app > Select a contact > Edit > Scroll down and select 'Add Another Field' > Message Tone
If not, please go to Settings > Applications > Application Manager > More > Reset App Preferences. Now, open the Messaging app > More > Settings > Notification Sound. Does it give you a option called 'Sound Picker' at this stage? If so, choose Sound Picker and hopefully your downloaded option should be available for selection. If you're still experiencing issues, try going to Apps > My Files > Internal Storage > Look for the folder containing the default notification sounds, and move your download into this folder.