At a muster at Finglas a week or so after the the Battle of the Boyne the Danish Troops in William III's Army were:

Horse
Colonel Jemel's Regiment
Colonel Jesnop's Regiment
Colonel Schescad's Regiment

Foot
Livgarde til fods (Dronningens) Regiment
Livgarde Grenadier Regiment
Prince Fredrick's Regiment
Prince Christian's Regiment
Prince George's Regiment
Zealand Regiment
Jutland Regiment
Zuitland Regiment

Although the Fyen or Funen Regiment (the way my book spells it) existed at this time, it was not included in this muster. Of course this doesn't mean that they didn't serve in Ireland. There may have had some sort of rotation system, or they may have been serving elsewhere in Ireland.

There were close links between the Danes and the Dutch in those days, and so the Danish Monarchy were happy to lend William most of the Danish Army. Of course, William would have paid for them (this was quite normal then).

I'm sorry that I can't provide any better information. Perhaps there is a Danish Army website or you can contact the Regiment concerned (or their successors). Britain has many regimental museums which would provide this sort of information. Perhaps Denmark has also.

I would be pleased to receive any more information you can find. I'll keep trying myself.

Les