although I am a Dwyer researching my own Irish roots, this is not a post about Dwyers specifically.
I am trying to understand your difficulty with the access to the Church?
Churches are under the governance of their denomination. For example, Roman Catholic, Presbyterian, Church of England, Quaker etc.
Not the government.
Where was the church and what was it's name?
If it was on private land, it sounds as if the church itself might have been deconsecrated and used as a home or a business?
Also, it is very unlikely you would have found any records there, as the historical records are centralised either in the national Archives in London (for English records) and might be found also in the family history society for that area.
These Family History Societies are online and will often have members whom can help you in your search.http://www.ffhs.org.uk
If you let me know the church and parish/county where they married (and when)..I will try my own records.