You did not mention the religious denomination of the family but from what I am seeing in available online church records, it looks like they may have belonged to the Church of Ireland.
What is available in church records depends on their denomination and where they were from and what has survived. Some records go back to the 1600's, some didn't start until the mid-19th century.
I see only four people called Porter in Cork in Griffiths Valuation (1840's-1860's - names Charles, Denis, John, Richard) - it is unclear whether one of these could be your gg-grandfather since none of these names were mentioned. There are several George Porters listed in northern counties.
The church records freely available online cover only a portion of Cork Roman Catholic records. North and East Cork RC records are available via fee-based sites, as are some C of I records. Many C of I records were destroyed in the 1922 Dublin fire.
You can check Griffiths online and search all of Ireland, http://www.askaboutireland.ie/griffith-valuation/
Also the church records freely online (with more records due to come online later this year),http://www.irishgenealogy.ie
And also check the fee-based sites:
Mallow Heritage Center,http://www.mallowheritagecentre.com/
Cobh Genealogical Project - for C of I records for Cork,http://www.cork.anglican.org/resources/genealogy.html
More info on Griffiths and church records here,http://www.corkgen.org/publicgenealogy/cork/genealogy.html
One possibility to consider is if a member of the family had a specialty trade or profession. If so, they could be listed in a city or county Cork directory. Some directories are online or partially online.
Or, taking a day to visit the fee-based site http://www.origins.net/
might be worth it for trawling through any Porter matches. (Costs maybe 9 British pounds for a 24 hour subscription.)
Still other possibilities are trawling through the Irish Times new archives:http://www.irishtimes.com/archive/
Or the Irish news archives:http://www.irishnewsarchive.com/
You can practice formulating your searches for free then if you think you see something you want to look at in more detail I think you can buy as little as a one day subscription.