Why don't you think a hunt makes sense?

To me it's the most logical explanation:
Hunts are/were frequently held on Sundays in Ireland.
You have a horse fair starting the next day, so there are even more horses around than usual.
The 'sport and kill' bit is in the version supposedly handed down from the original. I think it's more likely that there was simply a hunt than the lyrics of this song, which had originally been written down, were screwed up.

In any case, I hope someone who isn't just guessing (although I'm about 95% sure I'm right), will comment.