It’s great to hear that you are tracing your Irish Family History!
Before 1864 records were kept in the form of church and parish records
, all the surviving records have been sorted into county-based genealogical centers. After doing some research, the oldest record for the birth of a James Nichol
I can find is on 1867. There are some other records but of more recent dates so they might not be the record of your great-great-grandfather. However, it is very probable he was born in Belfast as this is the place with the highest number of Nicholl births.
Also, I did find a marriage record between James Nicholl and Margaret Thompson
in 1878, which you could be interested in.
Hopefully, our members can help you more with finding out about your ancestry. (Brian, are you there? )