Thanks so much for sharing this detailed image of the Massachusetts Naturalization record for Patrick, Laura!
It definitely looks like the name starts with a 'G', and is something along the line of Ganonturton. As Martin mentioned, there is no townland that is similar, but it is possible that the person writing down Patrick's information wouldn't be familiar with the spelling of his hometown, and wrote it down phonetically.
Before 1864 records were kept in the form of church and parish records and all the remaining records have been sorted into county based
genealogical centres. Since we don't know where Patrick Cunningham was born, I've had a look through the available
church records, and there were a few hits, but nothing really stood out.
Do you happen to have any other names from his relatives, like parents or siblings? This might be able to help us narrow it down.
Hopefully some of our experts can take a look at well, maybe they recognise the name from somewhere. :)