Ulster of course is wider than Northern Ireland, and "Orange songs" are only one of the traditions of Ulster or of Northern Irealnd.

But what is sometimes forgotten is that "Orange songs" don't just come from Ulster. It's just the nonsense of partition which gets in the way of recognising that the Orange tradition has been an all-Ireland tradition as well.

There's a good song called "The Orange Maid of Sligo" that is list in the Digital Tradition (though for some when you click on it, it won't come out into view), and there's "The Orange Lily-o", which is in no way a Belfast song so far as I'm aware:

"Oh did you go to see the show
Each rose an pink a-dilly-o
To feast your eyes upon the prize
Won by the Orange Lily-o
The Viceroy there so debonair
Just like a daffy-dilly,O
And Lady Clarke, blithe as a lark,
Approached the Orange Lily,O

Then heigh-o the Lily,O,
The royal llyal Lily-o
Beneath the sky what flower can vie
With Ireland's Orange Lily-O?

The elated muse, to hear the news
Jumped like a Connacht filly-o
As gossip fame did loud proclaim
The triumph of the Lily-o;
The lowland field may rose yield
Gay heaths the highland hilly-o
But high or low, no flower can show
Like the glorious Orange Lily-o

Then heigho the lily-o
The royal, loyal lily-o
There's not a flower in Erin's bower
Can match the Orange Lily-o
^^

And of course the "Ould Orange Flute" takes place both in Ulster and in Connacht.