Hi Tim and welcome to this great site and friendly forum.
From my various searches it seems I cannot offer any more data to what you've found, hopefully other forum users will tho....
Have you tried searching this site's free access PRs database for the Forest area ?
I have and cannot find a single one for the name DENEHY, or indeed some spelling variations of it. Similarly I cannot find any on the GlosBDM site.
What REALLY surprises me is that despite FreeBMD giving very full coverage of the Monmouthsire area, I can only find a couple of entries which may fit your family surname, searching "all types" from 1838 til 1888 !. The nearest match I can find is;

Surname Given Name District Volume Page Transcriber
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Births Sep 1884
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Denahay Thomas Peter Newport M. 11a 194 walj

That said, I do recommend you search this site yourself, in the unlikely case you haven't already. Sadly it only offers hits for precise spelling matches of any surname entered, so have to repeat with the various spellings, "a"s instead of "e"s etc etc.

I've also thoroughly searched FreeBMD for Helen/Ellen Connors/Conners within FreeBMD, clearly a far more common name and there are several within the Merthyr etc area thro the years, but sadly no matches for her marriage to Daniel.

???
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I'm not subscribed to Ancestry but using it's free search for Daniel gives some clues which just reflect the Census info you already have, and appear to match those on Family Search aka LDS which you've also used, I presume this is your family;

"United States Census, 1900"
Name: Daniel Denehy
Titles and Terms:
Event Type: Census
Event Year: 1900
Event Place: Youngstown Township, Precinct B Youngstown city Ward 4, Mahoning, Ohio, United States
District: 68
Gender: Male
Age: 42
Marital Status: Married
Race: White
Race (Original): W
Relationship to Head of Household: Head
Relationship to Head of Household (Original): Head
Number of Living Children:
Years Married: 17
Birth Date: May 1858
Birthplace: Ireland
Marriage Year (Estimated): 1883
Immigration Year: 1887
Father's Birthplace: Ireland
Mother's Birthplace: Ireland
Mother of how many children: 0
Sheet Number and Letter: 9B
Household ID: 195
Line Number: 62
Affiliate Name: The U.S. National Archives and Records Administration (NARA)
Affiliate Publication Number: T623
GS Film Number: 1241300
Digital Folder Number: 004117765
Image Number: 00939
Household Gender Age Birthplace
Head Daniel Denehy M 42 Ireland
Wife Ellen Denehy F 38 Wales
Son Thomas Denehy M 16 Wales
Daughter Maggie Denehy F 10 Ohio
Son Daniel Denehy M 7 Ohio
Son Garrat Denehy M 5 Ohio
Daughter Ivea Denehy F 1 Ohio

"United States Census, 1910"
Name: Dannel Denehy
Titles and Terms:
Event Type: Census
Event Year: 1910
Event Place: Youngstown Ward 4, Mahoning, Ohio, United States
District: 128
Gender: Male
Age: 55
Marital Status: Married
Race: White
Race (Original): White
Relationship to Head of Household: Head
Relationship to Head of Household (Original): Head
Birth Year (Estimated): 1855
Birthplace: Ireland
Immigration Year: 1886
Father's Birthplace: Ireland
Mother's Birthplace: Ireland
Sheet Number and Letter: 9B
Household ID: 185
Line Number:
Affiliate Name: The U.S. National Archives and Records Administration (NARA)
Affiliate Publication Number: M1283
GS Film number: 1375225
Digital Folder Number: 004449945
Image Number: 01067
Household Gender Age Birthplace
Head Dannel Denehy M 55 Ireland
Wife Ellen Denehy F 45 Wales
Son Thomas L Denehy M 24 Wales
Daughter Margret Denehy F 19 Ohio
Son Daniel J Denehy M 16 Ohio
Son Garrate J Denehy M 15 Ohio
Son Lenord Denehy

I also see other events re this family but only those you've already quoted. Unfortunately and as you no doubt know, there are clearly more than one Daniel D'y born in Ireland in the 1850s so tricky to untangle them.

However I've not seen ANY records positively linking them with Monmouthshire, perhaps if you post these records that might help us to help you. Perhaps you mean their relatives who stayed in Mons, for example, perhaps better this route is worth following ?

Similarly I've searched LDS for Ellen Connors, eg this which again I'm sure you've seen;

"Ohio, Deaths, 1908-1953"
Name: Daniel Denehy
Titles and Terms:
Event Type: Death
Event Date: 23 May 1915
Event Place: Youngstown, Mahoning, Ohio
Residence Place:
Address:
Gender: Male
Age: 20
Marital Status: Single
Race:
Occupation:
Birth Date: 24 Feb 1895
Birthplace: Ohio
Birth Year (Estimated): 1895
Burial Date:
Burial Place: Ohio
Cemetery:
Father's Name: Daniel Denehy
Father's Titles and Terms:
Father's Birthplace: Ireland
Mother's Name: Ellen Connors
Mother's Titles and Terms:
Mother's Birthplace: Wales
Spouse's Name:
Spouse's Titles and Terms:
File Number: fn 29713
GS Film number: 1983348
Digital Folder Number: 004095907
Image Number: 00985

==============

So, sadly at the mo I cannot offer anything new, altho other forum users may be able to do so as they're more experienced and capable than I am. HOWEVER as it looks like this query isn't particularly linked to the Forest of Dean, plus it's a very busy time of year while preparing for Christmas (the forum's been very quiet indeed recently) then you may have to be patient.

This relatively new Monmouthshire website may be worthwhile your browsing. Thanks entirely to your post I've found this site, so for that THANKS !!
http://www.monfh.org.uk/

Looking forward to your thoughts re the above findings and my questions, any more info you can give us can only help, regards, J

If it's any help,

on GR the General Register of BDM gives,

Daniel Denehy
Married 2nd Quarter 1883
Newport (Monmouthshire)

One of two possible spouses (i.e. on the same page)is,

Ellen O'Connors

Can see this family has a number of Public members trees on Ancestry

Thomas A's birth date is given as the 29 June - so Jeff's birth may be the correct one i.e.

Name: Thomas Peter DENAHAY (Daniel's father's name given as Thomas on D's death certificate, on Public members tree)

Date of Reg: July/Aug/Sept 1884

Reg District: Newport

Inferred County: Monmouthshire

Volume: 11a

Page: 194

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?

1881 Wales Census, Cardiff, St John -- 20 Sandon Place, Glamorgan - Cardiff, Monmouthshire

John DALEY - 56 - Coal Keeper ??? - born Ireland, Cork
Mary DALEY - 53
John DALEY - 26
Thomas DALEY - 17
Margaret DALEY - 13
Mary O'BRIEN - 40
Daniel DUMEY - 21 - labourer, born Ireland, Cork
John O'Sullivan - 26
Ellen SUTTON - 45
Catherine WALSH - 28
Jermemiah DALEY - 40
Ellen DALEY - 40

1881 Wales Census, Cardiff St John - 20 Park Place

working for Thomas U H PLAIN - Shipbuilder

Ellen Oconnor - 26 - General Servant, born Cork Ireland

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Ancestry (Marriage)

Name: Daniel DENERY

Date of Registration: April/May/June 1883

Reg. District: Newport

Inferred County: Monmouthshire

Volume Number: 11a

Page Number: 300