If you are on PC, grab the MP3 for the song yuou want, go into your oblivion data folder, and find the folder named "Music" If you only want that one song, delete the files in the Dungeon folder, then drag the MP3 in there. It will play in all Oblivion realms, and other dungeons.
I was under the impression you have to actually rename it the same way the original stuffs are :/
Also, to OP: yes, you can. What I did was put the songs I want to play and rename them the way the original files are, just in case, but it works and I don't complain. I use Final fantasy Tactics' and it works well.