Although there's no indication for prev marriages, considering the difference in ages between the children, and second one born apparently soon after the marriage date, the possibility of a previous marriage should be considered. I.e., this James and Ellen may be the ones sought, and James was married previously (previous wife also born Ireland, from birthplace of James Jr's mother).
It could be from a previous marriage or other circumstance. Did you notice the 1920 US Census for James McCoy Sr. and son, James McCoy Jr.? The 1920 Census has James Sr. born in PA rather than in Ireland.
Recorded as McCoy and sometimes McKoy, this interesting surname is of Irish, Scottish and Manx origins. It is a developed form of the Old Gaelic Mac Aodha, meaning the son of Fire, originally the name of a Celtic pagan god. The McCoys came to Ireland as gallowglasses, their home territory being the Isel of Man and the southern isles of Scotland such as Islay. In Ireland the surname is chiefly found in the Counties of Armagh and Monaghan with a sprinkling in County Limerick and even far away in Cork. (Click on address below for more information).
Yes, I did see it. It certainly looks like the same persons. Re: birthplace: I wouldn't think there's any significance. As I'm sure you well know, birthplaces of self and parents vary a lot from census to census.
However, maybe I'm misunderstanding the intent of the answer you posted. Are you saying that's not the same James McCoy (Sr or Jr), because of the birthplaces? James Jr in 1900 had both parents born Ireland. In the 1920 census (looked up) you posted, James Jr had both parents born Pennsylvania.
Regarding James Jr, the following provides another possibility. James Sr may have married previously another woman named Ellen who died before 1897. Unfortunately, I can't access the image itself as it's restricted but here's the index info.
Death certificates may or may not indicate his parents. Information on death certificates is commonly provided by an informant. If the informant doesn't know, it won't appear, or the information may be inaccurate or incomplete, though better information than none.
There are other possibilities, Hugh, such as obituaries and news articles that read "James McCoy was visiting his parents...". Obituaries are same as death certificates, however, as someone other than the deceased provided the informaiton. I have access to a couple newspaper sites. I'll take a look. EDIT - No joy. No hits for Philadelphia newspapers 1920-1955 for James or Ellen. Searching elsewhen and elsewhere comprises a few thousand hits. Sorry.
You can also look at the Chronicling America site, though the dates may be available.
"United States Census, 1920," index and images, FamilySearch(https://familysearch.org/pal:/MM9.1.1/MFYL-2HV : accessed 09 Aug 2013), James Mc Coy Sr., 1920.