Building on McCoy’s information about possible William Loudens in Coolshinney and Ballymoghan, I searched the 1831 census again. There were about 48 households in Coolshinney and 87 in Ballymoghan, but none named Louden or similar. Possibly your ancestors were labourers who moved about a bit. They can always be tricky to locate.
The Minister at Magherafelt 1st Presbyterian kept a visitation book. He went round all the homes in the townlands around Magherafelt in the years c 1820 – 1841. He did a mini census and noted who had emigrated or died etc. Those visitation books are in PRONI in Belfast. They are not on-line and a personal visit is required to view them. Here’s the records as per the PRONI catalogue:
Baptisms, 1771-81(with index), and 1813-1964; marriages, 1769-82 (with index), 1819-28 and 1845-1963; marriage notice books for Magherafelt Presbytery, 1845-1946; session minutes, 1703-82 and1818-56; committee minutes, 1848, 1852-3 and1911-
45; list of elders in 1828; ministers’ visitation books,1823-32 and 1841; ministers’ diaries, 1833-54; ministers’ account book, 1889-1904; history of the
congregation prepared in 1853. [Baptisms 1703-06 for Dawson's Bridge may include baptisms for 1st Magherafelt – see under P. Castledawson]
3rd Cookstown Presbyterian church has a marriage register for a number of Presbyterian churches in the general area and it includes some marriages for Magherafelt 1819-28. Copy of those records in PRONI. (They are not on-line anywhere so far as I am aware).