Eire2Go,
No it?s not a secret marriage. Rootsireland use a template for their marriage transcriptions and some sections are left blank when the relevant information isn?t available. So for an RC marriage in the mid 1800s all the church records will usually contain are the couples names, the date of the ceremony and the 2 witnesses names. So no parents names, no townlands (addresses) or occupations. So that?s why there are blank sections. Not that it was secret, just not recorded.
You can check when the RC records start by using the attached link. It also tells you where you can find copies:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/
In general copies of most of the church records for the 9 counties of Ulster are held in PRONI (the public record office) in Belfast. Further copies are held elsewhere eg RC records in the National Library in Dublin. Church of Ireland records in the RCB library in Dublin. Some (but not all) are on-line on various Irish genealogicla sites (mostly pay to view). In some cases however they are not on-line and the only way of accessing them is to go to one of the libraries or contact the Priest/Minister etc.
Some of the on-line transcripts contain quite a lot of mistakes. That?s for the usual reasons eg poor handwriting or human error. The best way to check is to obtain sight of the originals if you can.
Can?t immediately place Courinarran. Nearest I can come up with is Carrowncaran in Co Roscommon. Do you know which county or parish your place should be in? That may help me narrow the search.
I think your Brackey is Bracky, a townland of 1122 acres, in the parish of Termonmaguirk. You can see it easily enough using the maps on Griffiths Valuation which will also tell you who had land there in 1860. It?s between Omagh and Carrickmore. Probably about 5 miles east of Omagh. It?s not far from Beragh which was probably the nearest post office.
Not sure I can help you with the denomination if it?s not shown on the transcript you have bought. You could try e-mailing rootsireland and asking them. Otherwise try the 1901 census for the townland and see if the family were still there then. In which case their denomination will be noted, and so that should be a good clue.
Elwyn