Christine,
Variation in the spelling of places and surnames in Ireland is commonplace so expect to find that routinely. Having a single correct spelling was not a concept that troubled our ancestors in the 1800s. The parish name tends to be Killeeshil for RC records and Killeshil for civil and other denominations records. But not always.
Killeeshil RC baptism records for the years 1816 ? 1900 are on the rootsireland site. I assume that you have searched those for the couple?s children? If they are not there, and you think they ought to be, then it might be worth double checking by looking at the original documentation. There?s copies on microfilm in PRONI, Belfast and in the National Library of Ireland, Dublin. These microfilmed copies will be going on-line in mid 2015 (on the National Library site), if you can?t get there in person. Expect to find handwriting that is very hard to read, and so transcription mistakes on the rootsireland site are very common.
Apart from baptism records, there are not other relevant records in the mid 1800s which might mention your ancestors, so they are probably your best bet to start with.
Tradition was to marry in the bride?s church, so if by any chance James Conlin came from a different parish to Mary Laughran/Laughlin then she would probably have moved with him to his parish, and their children would therefore be baptised there.
Do you know the Conlin?s occupation? If farmers, then it?s be worth checking the tithe applotment records (1820s/1830s) for Tyrone, as well as Griffiths Valuation. (1860) which has several Conlon families listed in Killeeshil. Griffiths is on-line but for the tithe applotment records you need to go to PRONI in Belfast to look them up.
If you think James senior was still alive in 1864 or thereafter, then his death should have been registered. A death in Killeeshil would normally be registered in Dungannon. Searching the Irish civil indexes, 1864 to 1901 shows 3 Jas Conlon/Conlan deaths in that period, registered in Dungannon. One is of an age to be the father of James who married Mary L. (He lived 1792 ? 1879).
Elwyn