Andrew McIntyre married Ann McLeish/McLeich in Ballymoney/Ballymena

Kayemac,

You say that Andrew McIntyre was born around 1790. There aren’t many records in the area for that period. I did look at Park’s census of Ballymoney for 1817 and there were 2 McIntyre families there. One headed by William and the other by Archibald. Neither contained an Andrew.

From the background and surnames you have given, the families seem likely to be Presbyterian (so descended from Scots who settled in the area in the 1600s). No Presbyterian churches in that area have any baptism records for the 1790s. The likelihood of tracing the family from the information you have at present does not seem great. Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.

The North of Ireland Family History Society are running an Ulster DNA project and can offer FTDNA testing kits at a reduced price.  http://www.nifhs.org (Go to DNA project on the website).