Diane,
An Irish statutory marriage certificate contains the fathers names, but not the mothers. RC church records in early years don’t have any parents names but in later years they do. So their records vary.
Non RC marriages were recorded in the statutory records from 1845 onwards. I have searched them for a marriage between Hugh Mullen & Jane Stewart/Stuart but did not find one. RC marriages were only recorded in the statutory records from 1864 onwards. Prior to that you have to rely on church records. Not all have survived. I searched those that are on-line on Ancestry but did not find the marriage. The oldest RC church in Belfast is St Mary’s which opened in 1784 but which has no marriage records before the 1867. (They were either never kept or have been lost). So if the couple married there then sadly no record survives.
The absence of a non RC marriage in the statutory records points to them having married in an RC church. However those records have gaps as I have explained. If you know that the couple lived in Belfast and married c 1853, I’d suspect they married in St Mary’s RC.
Stuart and Stewart are completely interchangeable in Ireland. That was very common. The concept of a single “correct” version of a name is not one our ancestors would have recognised or been bothered about. There are many interchangeable names in Ireland and you can expect to see either version feature in the same family. So it’s wise to search Irish records using both versions.
Examples of interchangeable surnames, are Robertson & Robinson, Kilpatrick and Kirkpatrick, Nogher & Connor, Faulkner & Falconer, McConnell & McDonnell, Kerr & Carr, Stewart & Stuart.
The Mc & O’ prefixes on Irish names are detachable and were used and dropped on a whim. So for Mullen you need to include McMullen.
You may be told that Stewart was the Protestant version and Stuart the Catholic (or vice versa). Complete nonsense. Search the 1901 or 1911 Irish censuses and you will find both spellings used by all denominations. (1084 people named Stewart in 1901. 307 were RC, the rest Protestant. 8774 Stewart of which 981 were RC. So the 2 names are predominantly Protestant but both spellings were used by RC too).
http://www.census.nationalarchives.ie/search/
Griffiths Valuation is largely a record of folk who lived in rural areas. Not many people in towns are recorded. Unless you have information suggesting your family lived in Dunaghy I would discount them.