Searching for my 3GGP, George Robinson , cooper by trade and Mary McCombe (1786-1873, Mar 8, 4 Dark Lane , Derry City )

George’s birth was long before the start of statutory birth and death registration in Ireland (1864). So you would need to rely on church baptism records for his birth (if they still exist) and there may be no record of his burial unless he happened to be Church of Ireland as most other denominations didn’t keep burial records.

RC records are mostly on-line on the nli site:  

https://www.nli.ie/en/family-history-introduction.aspx

For other denominations, the churches usually hold the originals but there are also copies in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:

https://www.nidirect.gov.uk/publications/proni-guide-church-records

If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net

The 1831 census of Co Derry has survived and I see the following entries for people named George Robinson

http://www.census.nationalarchives.ie/pages/1831/Londonderry/Kennaught/Tamlaghtarde/Milltown/1/

http://www.census.nationalarchives.ie/pages/1831/Londonderry/Loughinshollin/Kilrea/Kiltrea/156/

http://www.census.nationalarchives.ie/pages/1831/Londonderry/_/Templemore/Creevey/11/

The one in Creevey (now standardized as Creevagh) seems most likely to be your family. It’s on the outskirts of Derry. There were 10 in the family, all Presbyterian. So George is probably in a Presbyterian or Church of Ireland graveyard in the general area.