Thomas Boyd b~1785 ireland d in New York (Brooklyn), m Leticia Wallace b~1786 ireland d in New York (Brooklyn),
how do you know they were born and married in the north of Ireland?
children location of birth unknown, and in no particular order
Margaret Ann Boyd your Great x2 grandmother.no dates ?
Thomas Boyd Junior, no dates
Jane Boyd no dates
possible Nancy Boyd that immigrated to New York in about 1839 or 1840
possible (Hugh)?
Unless your names turn up in some existing family tree the lack of irish records means its going to be a very difficult search in which many give up unless lucky enough to find a church record etc to get to a church record you need to find a county and then a civil or religious parish.
take a national record for example which in itself excludes most of the population
Flax Growers Of Ireland 1796 gives a hint of which Ulster Counties both names Boyd and Wallace were living
the website to use is for Co Antrim
http://www.failteromhat.com/flax/antrim.php and then substitute the next county in that website etc
Co Antrim Yes both
Co Armagh Yes both
Co Cavan Yes But Less
Co Derry Yes both Co Derry used in that website record in other records Co Londonderry
Co Donegal Yes both
Co Down Yes both
Co Fermanagh Yes both But Less
Co Monaghan Yes both Less Wallace
Co Tyrone Yes both
to find somepathway to where they got married, if they married in Ireland, its most likely they came from the same county so one could download all the entries findable in the flax growers lists say ove 250 entries, sort them by county and civil parish you will get matches by civil parish, that’s again most likely if Thomas sr was the son of a Thomas you might find him or a namesake. its finding a possible parish to look up its church records that is the purpose of all this
there are many boyd family trees in existence see ancestry etc
trying to be helpful
good luck