Don't run with Honora quite yet.
How I got there:
(A) Found a James Crowley marriage in Jackson, MI, in 1893, using FamilySearch (that's the link). This listed parent's names for both parties. Actually, father's name and mother's maiden.
So one piece of data says parents are "James Crowley" and "Unknown Sullivan".
(B) James is listed in 1900 with a Jan 1864 birth. 1920 looks like same person, but James "C" Crowley 1900 also list married for 7 years to Maggie (hence 1893 marriage record probably OK.)
(B+) Your latest comment says your looking for James "C" , so we've got the right family.
(C) I subscribe to a site called "RootsIreland.ie". You need an account (free) to search but need to pay to really see the detailed record. You can still find a lot with the free search.
For example: "No James Crowley in Cork with James for a father (between 1864 +/-2)"
So, James may not have been Baptised (assuming R.C.) in Cork, or not born between 1862-1866.
(D) Another search was just for the parents; i.e. surname=Crowley, father=James, mother surname=Sullivan, (1864 +/-2):
This yielded 2 females. (I checked the detailed record, I've got a subsciption.)
Marion (morther=Nora) Co. Tipperary
Mary (mother=Honora) Co. Waterford
(E) Finally, I looked for James Crowley, father=James, Mother=Sullivan, no date restriction
I was surprised to get 2 results in 1859
James (morther=Honora) Co. Tipperary
James (mother=Honora) Co. Waterford
(F) there are numerous James Crowley during this period, 1864+/-2 but not with James & Sullivan for parents.
It is all based on 1893 marriage record. Could really use:
(a) Another document with parent's name, particularly mother's given name. (James' death cert. for example)
(b) James arrived (per 1900 census) in 1883
- did he come alone?
- are there Naturalization papers?
(c) did any siblings come along/arrive later? (Like a Marion or a Mary)
- I doubt he was an only child, farm families in 1800-1900 weren't small.
So ... tempting data but no solid proof, a couple of interesting leads though.