The community of sharing is certainly always eager to provide new avenues of Cody exploration! A few more pieces of information may well assist to help others with your query re the Irish Cody family in Armagh, so don't hesitate to let us know whatever pieces you may have that could turn out to be significant.
When were your father (William Cody) and grandfather (also a William Cody) born? Do you know the given name of your Cody grandmother, or anything about her that would help to sort the vast number of William Cody males in/from Ireland? Yes, there was a William Cody who married in Armagh, and indeed he may have had a son named William. You stated that, as I understand, that your grandfather was born in Armagh, but where was your father born? Do you have middle initials (or dates of birth/death) for either your father or grandfather, both having the name of William Cody?
However, importantly, there is no "Irish side" (per your inquiry) to Buffalo Bill's Cody ancestral lines by the Cody surname. Most folks simply don't realize that his "Cody" family (not from Ireland, and not even with the original surname of Cody) was already established in the USA (MA) in the late 1600s; so naturally with those Cody families who immigrated here in the subsequent centuries there has never been any connection by that common surname. Nevertheless, there are many reputable genealogists and credible researchers familiar with the Irish Cody families, inclusive of those who authored numerous texts covering those areas.
Keep on asking - and don't forget to provide any other details that may help others reach out to....help you! :)