There aren't county records in Ireland although many sources of information are by county.
Civil registration of births, deaths and Catholic marriages began 1864 (from 1845 for other marriages). For earlier information, as in this case, you need to find church records (if they exist). To do so you usually need to know the family's religion and where they lived (parish if not actual townland).
However, in this case there are several possible ways to find more information. First of all, if there are lots of descendants of the couple checking each branch to see what information they might have might be worthwhile.
Secondly, if Sarah's family were well-to-do (which is not nec. the case) there might be Wills, newspaper records, etc. about her family available. In the case of a mixed, or frowned upon, marriage it is quite possible that no wedding announcement will appear in the newspaper (for such an early date the Belfast Newsletter might be the only one available).
P.S. Sarah's family would have been Church of Ireland if they lived in County Tyrone not Church of England.