William Stewart & Ann Wiggins

The births and, presumably a marriage, are all long before the start of statutory birth registration in Ireland (1864) and marriages (1845).  You would therefore need to rely on church records to try and locate this couple.

You haven’t said what denomination they were, but judging by the 1901 census for the county, the Wiggins were almost certainly Church of Ireland as all of the 72 people listed there are Church of Ireland or Methodist. (Methodism is an off-shoot of the Church of Ireland but didn’t get established in Ireland as a separate denomination until 1816 for baptisms and 1835 for marriages. Your couple pre-date that. So you should focus on Church of Ireland records for Ann and the marriage).

A fragment of the 1821 census of Fermanagh has survived (and is on the same site as the 1901 & 1911 censuses) but there are no Wiggins listed in it.

Stewart is amore common name with 137 in the county in 1901 and they encompass all denominations ie Church of Ireland, Methodism, Presbyterian and Roman Catholic. There’s also 8 Stuart which is obviously just an alternative way of spelling the name. There’s 12 Stewart/Stuart in the 1821 census fragment.

There’s about 30 Church of Ireland parishes in the county and only about half have any records for the period you are interested in. A lot of early Church of Ireland records were lost in the 1922 fire in Dublin where, ironically, they had been sent for safe keeping.

You can try some of the pay to view/subscription sites like rootsireland for the baptisms and marriage but they don’t have all the surviving records, nor all the years. (Many tend to have 1840 onwards). The most complete set of Church of Ireland records for Fermanagh is in PRONI (the public record office) in Belfast. A personal visit is required to view them, as they are on micro-film.

Looking at the 1901 census of Fermanagh, I see that the Wiggins/Wiggans listed there were only in 9 townlands. You might want to identify the parishes that go with each townland, and start with them. The census is here:

http://www.census.nationalarchives.ie/search/

And you can see what parish each is in using this site:

http://www.thecore.com/seanruad/

RC records for Fermanagh are on the nli site. For Presbyterian records you should go to PRONI.(If you can't get there, you may need to employ a researcher).

If you can’t find your ancestors in the surviving records, there aren’t many other records to fall back on for the 1700s, and you might need to rely on DNA testing in the hope of matching with a family who know more about their ancestors.