Demoy doesn't show in any land records for Ireland from 1846-1864 and in Galway in 1855. Nor in any other Counties.
The only record I could find for the spelling was
a passenger record:
Timothy Demoy, age 21 Gentleman, Queenstown Cork to *Boston, Mass. Single date April 24, 1891 ship Samara.
1935 US Census, Middlesex, Masss. Catherine Demoy born in
Checked the Tithe Applotments 1823-1837 0www.genealogy.nationalarchives.ie
Checked the 1901/1911 Census www.census.nationalarchives.ie
In the UK 1871 Census are spellings as Damoy, Damoye, Demoy,but all born in France living Middlesex-London or Jersey, Channel Islands.
In the 1861 UK just one DeMilton, Kent, Park Place Gravesend
The US Census does have the name Demoy in the 1900 Census and indicate born in Ireland or Northern Ireland.
Timothy Demoy 1857 Catherine 1863 and another
Katherine born Aug 1871, Ireland
but also another John Demoy born in Holland.
There were lots of Moy's born 1872, 1875, 1881, noted in Stranorlar and Glenties, Co. Donagal and Tobercurry
I wonder with the names in the UK if the name deMoy was a family in Ireland, often changed french/norman names such
as D'Arcy to Darcy.No luck with that either.
Looked at www.landedestates.ie
for the name Demoy or deMoy
nothing there (so where did the gentleman Demoy come from in 1891) A gentleman was not nobility, or even gentry but
usually had large leases of land off the nobility and would then collect rents from their tenants, some were ex-military
Captains etc., Ministers who were given land by land owners
to build a church and then rent the lands for income.www.emeraldancestors.com
(Northern Ireland) has no Demoy nor is there any of that spelling in the Northern Ireland telephone book.www.rootsireland.ie
does have both parish and civil registrations up to 1900.www.familysearch.org
1864-1950's you can search Ireland as
I did or America, also England.
I don't know what else to suggest.
I am not able to check the phone book for Ireland at this time as my viewer isn't working.