IrishGenealogy.ie - Dept of Arts, Heritage, Regional, Rural and Gaeltacht Affairs

Robyn, your desire to emphasize the website and its database is understandable. If you have numerous entries from this site, that approach would prevent bloating your source list with all the individual records from that site.

Because this source has open access, I've backtracked your source to see for myself exactly all the details that the site provides. I do see a couple of additional "identifiers" that seem to be essential. Also, clarity might be better achieved by placing the details in more-standard order, keeping details from each layer within its own layer:

Layer 1:

Department of Arts, Heritage, Regional, Rural and Gaeltacht Affairs, "Civil Records," database with images, IrishGenealogy.ie (https://www.irishgenealogy.ie/en/ : accessed 25 September 2016), image, marriage registration of John Law and Maggie Keys, 5 September 1905, Church of Ireland’s “Lack or Colaghty Church,” County Fermanagh;

Layer 2:

registration recorded 16 October 1905 by James Waterson, Clergyman, in Irvinestown Registration District, unidentified register, folio 113?, “second page,” stamped no. 05701003, entry 179.

To put them together, we would have

Department of Arts, Heritage, Regional, Rural and Gaeltacht Affairs, "Civil Records," database with images, IrishGenealogy.ie (https://www.irishgenealogy.ie/en/ : accessed 25 September 2016), image, marriage registration of John Law and Maggie Keys, 5 September 1905, Church of Ireland’s “Lack or Colaghty Church,” County Fermanagh; registration recordeded 16 October 1905 by James Waterson, Clergyman, in Irvinestown Registration District,unidentified register, folio 113?, “second page,” stamped no. 05701003, entry 179.

This still leaves us with one piece of data provided by the website’s database entry that we haven’t placed into the citation: “Group Registration ID 2044640.”  According to a discussion of this database at http://www.irishgenealogynews.com/2014/07/new-irish-civil-registration-indexes.html, this number is a unique identifier assigned by the database to each individual registration. As such, a logical way to incorporate it into the citation would be this:

Department of Arts, Heritage, Regional, Rural and Gaeltacht Affairs, "Civil Records," database with images, IrishGenealogy.ie (https://www.irishgenealogy.ie/en/ : accessed 25 September 2016), image, marriage registration of John Law and Maggie Keys (5 September 1905, Church of Ireland’s “Lack or Colaghty Church,” County Fermanagh), citing Group Registration ID 2044640; registration filed 16 October 1905 by James Waterson, Clergyman, in Irvinestown Registration District, unidentified register, folio 113?, “second page,” stamped no. 05701003, entry 179.