Dear Catherine:
Many thanks for your post to the Ireland Reaching Out message board.
Your best bet is to stop into the Clones Library and to look for Caitriona Lennon who works there. They have a very good local history section. I am not aware of whether or not they have parish registers but I do know that the National Library has the parish registers online for many parishes in County Monaghan. Ematris parish can be accessed here: https://registers.nli.ie/parishes/0307
You mentioned that the first child born to Thomas & Catherine was born in Monaghan. If that is the case, have you checked the Irish Genealogy website for a marriage record? You may need to look outside the Monaghan area due to some transcription errors in the uploading of the records.
I will forward notice of your trip to Caitriona Lennon and I will also include her email address in this post if you would like to contact her directly. Please let me know if you need anything further.
Here is some information about the collection that may assist you:
http://www.askaboutireland.ie/reading-room/culturenet/archives/monaghan/monaghan-county-library-l/index.xml
Have a wonderful trip and please keep us posted as to your progress.
Kind regards,
Jane