To find John?s baptism, you need to know his denomination. Do you know that? Looking at the 1901 census for Co Down there are over 200 Fultons and they are a mix of Church of Ireland, Presbyterian and RC. So hard to say.
For the marriage, tradition was to marry in the bride?s church. So do you have any idea of her denomination, or where she came from? Again looking at the 1901 census for Co Down the majority of Guthries are Presbyterian but there are a few Church of Ireland too.
If you have no idea about the denominations, then I would start by searching the various church records for Hillsborough for John?s birth. Though some Co Down baptism records are on-line, not all are, and you will probably have to go to PRONI (the public record office) in Belfast to check every denomination for Hillsborough.
The problem you are going to encounter is that if the marriage or any of the 3 baptisms was Presbyterian, the relevant records may no longer exist. Hillsborough Presbyterian church has no baptisms earlier than 1833, and no marriages before 1845. Nearby at Annahilt Presbyterian church they do have baptisms from 1780 but marriages only from 1838. Hillsborough Church of Ireland does have baptism and marriage records for the years you want, so you might be ok if either was of that denomination. If either was RC then there don?t appear to be any records for the years in question.
If you don?t know where daughter Elizabeth was born, then all you can really do is hope it was Hillsborough and search for her baptism, starting with the assumption she is likely to be the same denomination as her father. (It?s worth checking all the Scottish censuses to see if her place of birth is ever given in more detail than just ?Ireland.? Sometimes you get a townland or parish.)
You can see what church records exists for Hillsborough on the PRONI website:
http://www.proni.gov.uk/index/research_and_records_held/catalogues_guid…
There's a Margaret Fulton of Hillsborough mentioned on this useful Co Down website:
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/
