Cathy,
You say that you think the family may have been Presbyterians. That is statistically very likely, given that a huge percentage of the population of Co Down are descended from Scottish settlers, and it is undoubtedly a common Scottish name. That could well support your suspicion that the family were Presbyterian. Unfortunately there are no Presbyterian records for Downpatrick for the 1700s, and so that possibly explains why you cannot find his baptism. You could check the Church of Ireland?s records which go back to 1733 (with gaps). They are on the rootsireland site (pay to view). (In contrast to other Scots, many Reiver settlers adopted the Church of Ireland. Presbyterianism hadn?t taken hold in the borders, which at the time were a fairly heathen area religiously (and in other ways), and so it appears many of them arrived with little affiliation to Presbyterianism or any other denomination. Later they often joined the Church of Ireland).
Your ancestor won?t have been baptised as a Methodist, as there were no Methodist baptism in Ireland in the 1700s. Methodism took a lot longer to become established as a separate denomination in Ireland than was the case in England. In Ireland there was considerable resistance to separating from the Church of Ireland. It was 1818 before Methodists could conduct their own baptisms. However because of the continuing loyalty to the Church of Ireland and other factors, many Methodists continued to use the Church of Ireland for sacraments for many years after this date and it was 1871 before all Methodists routinely performed their own baptisms.
Regarding of the spelling of the surname, the idea of a single or correct spelling for a surname or a place name is very much a recent phenomenon and before that, especially in Ireland, there was no consistency. Names were spelled phonetically and each variation was down to the whim of the particular person recording the information. You will often see the spelling change as the records go back. This rarely indicates a particular deliberate decision to alter the name nor even a mistake. Not everyone was literate, but even when they were, exact spelling simply wasn?t something they bothered about.
There are some Clendinnings in Co Down on the Rosdavies site:
http://freepages.genealogy.rootsweb.ancestry.com/%7Erosdavies/
Elwyn