I just got this to work, if you want to use music or a downloaded .mp3 file a your text message notification you can create a new directory for them on your SD card using a file explorer. I used es to do this.
First create a folder called media then audio then notifications. Media/audio/notifications.
Then copy whatever file you want to use and put it in the directory under the last notifications path.
Then when you go to your notifications to change them the files will show up in the stock notification picker.
Hope that helps!
Edit:
I Just played around with this some more, I found that you can also add the paths ringtones and alarms to the last notifications sub folder & copy or move whatever audio file you want into them & they will also show up in the corresponding stock notification picker for each.
Silly me, at first I was trying to move or copy mp3's and audio file into the root system folder. I know I don't have root access for that, so it kept failing.
So I just created the same path it had in the SD card that was in the system folder where all the default sounds are stored, media/audio/notifications ringtones alarms, and sure enough, it worked.