I am going to try and write some more songs and invite everyone else to have a go too.
Well, you asked for it. I have no experience whatsoever, but this came to me last night (as I was trying to fall asleep--very annoying). I was thinking it would be both lore-friendly and a nice nod to players of past Elder Scrolls games to have songs that recapped the events of those games. This one is very much designed for increasing numbers of singers to join in on the chorus sections:
"Down to Our Last Septim"
Now hear me tell, of gates of hell
To Oblivion, to fire
The realm of Mehrunes Dagon
The monstrous Daedra liar
His assassins came, King Uriel was slain
The clannfears did run wild
While the dragonfires sputtered
For want of a Septim child
We were down to our last Septim
Hidden from evil eyes
Down to our last Septim
'Twas Martin, the wise
First at Kvatch, Dagon met his match
A Champion and a priest
With an ancient blade, who gave them aid
To thwart the dreadful beast
We were down to our last Septim
In the temple of the cloud
Down to our last Septim
'Twas Martin, devout
Gate after gate, they were set straight
The work of the Champion
While Martin made ready
To do what must be done
We were down to our last Septim
In the tower of white gold
Down to our last Septim
'Twas Martin, the bold
And then reborn, in dragon form
Martin did take flight
And banished Mehrunes Dagon
To the cold darkness of the night
We were down to our last Septim
And then, he was gone
Down to our last Septim
And so we sing this song
Yes we were down to our last Septim
We drink to him this night
Down to our last Septim
We'll be broke before first light
Use it or not as you wish; at best, it could probably use refinements and additions--please feel free to use or modify it according to a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
That would be a fairly contemporary tune. It strikes me that songs based on older events could be used in one of two ways. By default, they could simply be additions to the repertoire of the bards, as you've talked about here. But I could also imagine the songs being used in some sort of Bard's College mod--where you'd have to find songbooks in various Nordic barrows, and deliver them to the head of the Bards College, before the newly-discovered "ancient" songs could be unlocked and played by bards in the taverns.