Normally I would think that is a pretty big jump in speculation but you are probably right if you are
sure that Francis and Jeremiah are related. If so moved from Cavan to Fermanagh.
Parish records are how you will tie families together, some are on line. see below
In the Tithe Applotments (for tax) now a census substitute are 5 Hayes occupying property
1826 Frans Hayes, Parish of Templeport, Townland Tonerevan
1826 Francis Hayes, same
(could be a repeat because of the spelling or Francis could have two leases - These records are not complete as the originals at the National Archives, where the property details are listed as well like the Griiffith Valuation.
Griffith Valuation (tax) now census substitute 1857 in Fermanagh
Jeremiah Hayes, Parish of Kildallan, Townland *Breandrum, Poor Law Union of Bawnboy
tenant of Capt. Bedel Stanford
# 1 land 2 acres 0 roods 30 perches
#2 house, outbuildings and land 20.2.20
Same details but for Townland is Carn
#4 land 7.0.34
The name Jeremiah isn't as rare as you might think 54 at the time of Griiffith Valuation and 9 Francis but at least they aren't the usual, John, James, Patrick.......
Joseph Darling, Parish of Castlerahan, Townland Cornahilt, Poor Law Union Old Castle, tenant of
#34 Dublin St. Town of Ballyjamesduff - a house
William Darling, Parish of Crosserlough, Townland Duffcastle, Poor Law Union Cavan, tenant of
2b - a house
A Poor Law Union covered an area of no more than 12 mi. from the named town and administered to all Parish's towns, townland, villages within that boundary. Later Civil Registrations 1864+ used the same basic boundaries
I didn't look in the Directories 1824 or 1846 as farmers didn't appear in the directories till 1881 & 1894 www.failteromhat.com
Slater's Royal Directory:
1894 J & J. Darling, Newtown-Butler (mentioned in BT phone book) Farmer
Newtown-Butler is a small town in the Clones Union.
The British telephone book for Northern Ireland has 50 Hayes listed but none in Fermanagh, No Darlings
The Irish telephone book for Cavan has no Darling in Cavan but 36 listed in the Republic, Co.Kildare, Wicklow, Dublin........
Today another poster gave the website of www.fermanagh-gold.com
+ county (Fermanagh or Cavan)
Northern Ireland has two parish websites, both you pay, one is a not for profit foundation:www.rootsireland.ie
for civil registrations 1864+
Jeremiah Francis Darling born 05 October 1871 Cavan Fa: William Darling Mo: Mary Anne Hayes
Margaret Jane Darling born 03 December, 1869 Beandrum, Cavan parents same
Male child Darling born 13, July 1876, Cavan Fa: William born Buandrum Mo: Mary Anne Hayes
Female Child, Christening 16 Sept, 1874, Ballyconnell, Cavan
Susan Maltilda Darling, 24 June 1878 Killymachen, Fermanagh
Fa: William Darling Mo: Mary Ann Hays
Mary Ann Darling (Hays rather than Hayes) 29 May 1880, Killymacken, Fermanagh
Fa: William Darling Mo: Mary Ann Hays
Often births took place at the mothers, mother's home as hospitals were rare and christenings/baptisms took place quickly in RC households as compared to CofI. Usually CofI
would be the first Sunday after the birth and sometimes later, probably depending on circumstances.
Spellings can be different, LDS students copied from the National Library records, also would be hard to read some writings and often guessed a spelling rather than leave letters out.
General Registry Office, Dublin www.groireland.ie
you can get a certified birth certificate
if you can find a marriage certificate it would have both William & Mary Anne's father's names.
Only birth certificates would have mother's maiden names, parish records would probably have both but some parish's didn't bother with parents names.
Death Registered Jan-Mar 1909 William Darling age 61, Lisnaskea,Fermanagh
birth year 1848 based on age given at death (not always accurate)
2 Killymackan (Crum, Fermanagh)
Mary Anne Darling 61, born Cavan, Church of Ireland, Widow
Jeremiah Francis 39, born Cavan, age 39, farmer (est 1871)
Selina 23 born Fermanagh, seamstress (1888)
Sarah 20 born Fermanagh, seamstress (est.1891)
John Robert 17, born Fermanagh, Farmer (est 1894)
Mother didn't fill out how many children born and how many living.
Didn't find John Robert, Sarah or Selina in the LDS
I was told by a now Catholic but 200 year ago a CofI family it had to do with land reform and keeping their land, I'm sure there were lots of reasons.RC & CofI might change religions a couple might marry but children brought up RC.
Don't know if this is of help or you had it already.