Firstly, you can't assume Mary's father wasn't dead if he's not listed as deceased on the marriage certificate. It may be that the officiant never asked her or it just wasn't written down.
Secondly, by 1941 and certainly quite a bit earlier I would expect only a very, very, very small percentage of deaths to go unregistered.
Next, the vital records (births, marriages, deaths) on Irish Genealogy only go up to 1921 for Northern Ireland counties. After that date you need to look in GRONI's database (deaths 50 years old and older will be listed in the online database).
Lastly, you haven't mentioned here what denomination Bernard Naan and his family would have been but it was usually only the Church of Ireland that kept a burial register. Even today not all churches keep such records. Also, bear in mind that few clergy respond to requests for information- they are usually from outside the area and don't have time to do research as many cover more than one congregation.