To me, the name on the marriage entry looks to be an abbreviated Patrick. But since Patrick and Peter are largely interchangeable it wouldn’t really matter which. I’d say there’s a reasonable chance that it's your couple. Your problem then is finding out anything more about them. There’s no address, occupation or parents names. You have no easy way of finding out whether they were born in Belfast or had recently arrived there from the country (as so many people did at that time). In 1780 the population of Belfast was 13,000 (with just 300 Roman Catholics) and by 1900 it was 349,000. That gives you an idea of the flow of people from the countryside to the city during the 1800s.
You could have a look for Campbell deaths from 1864 onwards, in Belfast. I can see 12 Peters and 43 Patricks. There’s about 28 Rose, Rose Ann & Rosanna. When you strip away the ones who were too young or too old to be your couple, there’s probably about 10 worth looking at. Those from 1891 onwards are on-line free on the irishgenealogy site:
https://churchrecords.irishgenealogy.ie/churchrecords/
But for those prior to 1891 you will need to pay GRONI to see them. You can view the original certificates on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
Irish death certificates don’t contain that much information so it might be difficult to tell whether you have the right death, unless the spouse happens to be the informant. One positive thing is that if they had a child Elizabeth in 1863 then both Peter and Rosana seem likely to have been alive when death registration started on 1.1.1864. So as long as they died in Belfast, two of those certificates should be for them.
I’d say that getting back another generation prior to Peter and Rose Ann will be very difficult, if not impossible.
You mention that Campbell is a common Scottish name and that your ancestors might have been Presbyterian (at one time). Campbell is a common Scottish name. It’s also pretty common in Ireland. Looking at the 1901 Irish census there were 14,143 Campbells in Ireland of which roughly 7000 were RC. The remainder were Protestant, the majority Presbyterian (so pretty definitely of Scottish origin).
According to this site: https://www.johngrenham.com/surnames/ the name Campbell was:
Very numerous: Ulster in particular. This relates not only to the great Scottish clan, Scots Gael: Cam-béal (crooked mouth), but also the Ir. Mac Cathmhaoil (battle chief). These were a sept of Cineál Eoghain in Tyrone. In Donegal there was a Scots galloglass family called in Ir. Mac Ailín, who were also Campbells. MIF.
Large numbers of Campbells were invited from Scotland to Ireland in the period 1200 – 1400 as mercenaries (known here as galloglass) to fight for various Irish chiefs who were always squabbling over land etc.. They would have been RC since it was pre-Reformation, and many settled around Donegal & Tyrone. They were granted the land in return for their fighting skills.
Then in Plantation times (1600s) other Scots arrived, the majority of whom were lowland and Presbyterian. Belfast was largely built by lowland Scots settlers which is why there were so few Catholics in the city in the late 1700s.
So your Campbells could be native Irish (the battle chief clan), or of very old Scottish origins (galloglass). They’d all likely be RC. Or they could be of Presbyterian origins arriving in the 1600s but they would have had to switch to RC at some stage.
In the 1830s both parties to an RC marriage would have had to be RC. As you say when one converts there’s usually an adult baptism about a month before the marriage. Tradition being to marry in the bride’s church, if the groom came from a different parish or even a different church within the same parish his baptism might be there rather than in the bride’s church.
