Marriage certificates were only introduced in Ireland in 1845 so if Zachariah & Rachel married in Ireland in the 1830s, there is no certificate to find. You might find an entry in church register, but not all pre 1845 records have survived and many of those that do still exist are not on-line.
You mention the Black family having land near Dungannon. I checked the tithe applotment records (a series of records created for tax purposes which list most folk with land) and there were no Black households in the parish of Drumglass, which includes Dungannon, in 1832.
http://www.irishgenealogyhub.com/tyrone/tithe-applotment-books/parish-of-drumglass.php
What religious denomination was your family in Ireland?
I have one possible clue for you which is that in the 1901 census there was 1 Zachariah Black in Co. Tyrone. (There were only 9 people named Zachariah in Ireland in 1901). Families tended to repeat the same names, generation after generation, so it’s just possible the Zachariah in the 1901 census is distantly related to your Zachariah:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Ballynasollus/Beltonanean/1730464/
He was Church of Ireland lived in the townland of Beltonanean, in the parish of Kildress, Co Tyrone. That’s about 15 miles from Dungannon.
Zachariah in the 1901 census had a father named William Black. Probably not the William b 1787 but evidently a family name.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1900/10352/5768488.pdf
William died in 1879 aged 74, so born around 1805, give or take a year or two. (Most ages then were just guesses).
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1879/06520/4878271.pdf
Kildress Church of Ireland records start in 1794 (for baptisms & marriages). They don’t appear to be on-line anywhere but there is a copy in PRONI (the public record office) in Belfast and so you could look them up there to see if your Zachariah is listed around 1811. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net