There are six popular napoletane canzoni that I found with the title beginning "Core... (Cuore ...).

Core furastiero - Cuore forestiero
Core signore - Cuore signore
Core Napulitano - Cuore Napoletano
Core 'ngrato - Cuore ingrato
Core 'e Mamma - Cuore di Mamma
Core spezzato - Cuore spezzato

I can post the words in both Neopolitan and Italian, but I stay away from download sites.
Here is the website with the lyrics; Guest Paoloduddi can look at them and decide which one he is looking for.
http://medivia.sele.it/inglese/canzoni/index.htm
Canzoni