Miranda,
You can use this website to see where the 2 surnames were most common in Ireland in the mid 1800s. Both are largely associated with the counties of Ulster, so that seems the area to focus your search.
https://www.johngrenham.com/surnames/
You haven’t said what denomination your ancestors were, but that is another important factor. I suspect they were Presbyterian or Church of Ireland (ie Episcopalian). If so that also points towards Ulster (being the area where most Protestants settled).
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 is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).