Not sure if there's a connection here but why do you think Mary Clyde was born in Scotland?
Solomon, not that common a name, has been handed down in several generations of the Clyde family who belonged to First Garvagh Presbyterian Church.
Unfortunately, names of parents or a townland aren't listed in the early marriage records. One of the earliest Clydes I have is Thomas Clyde (c1757-1834) from Gortfad (just outside Garvagh) who I believe to be the father of Samuel Clyde of Gortfad. That Samuel had a son Solomon Clyde (c1820-1876), grandsons Solomon Alfred Clyde (1869-1942) and Solomon Clyde (1868-1893), great-grandson Alfred Solomon Clyde (1902-2000).
There is also a lease in Lord Garvagh's papers dated 1800 for John Clyde of Bellruy with two sons mentioned- John (eldest) born c1793 and Samuel born c1795. So, the family have been in the area for quite a while.
PRONI, and Coleraine Library (box #74), do have microfilmed records for Balteagh Presbyterian Church-
Baptisms 1868-1932
Marriages 1845-1936
Communicants 1890-1957
Teasurer's notebooks 1832-1846