Seeking immigration & naturalization records of Carmine & Michael Rossi

Hi all, maybe someone can kindly point me in the right direction here. I have been researching my great grandfather and great great grandfather. My great grandfather died in NYC in 1912 (i have his death certificate and date of birth). My great great grandfather bought his son's burial plot a few days after his son's death. I learned this from researching the cemetery deed. I have been trying to find my great grandfather's immigration/naturalization records and I've hit a complete road block. Also, I have been unable to find any reference to either my great great grandfather or his son in any of the census data, either Federal or NY State. I've also come up blank in reviewing the City directories. This is frustrating because I do have my great grandfather's address in Manhattan from the death certificate. I also suspect that my great great grandfather continued to live in NYC after his son's death because he gave permission to a third party from Manhattan to inter an infant in my great grandfather's grave. I've done a significant amount of searching on Family Search and Ancestry and a lot of the public sites, but i cannot find anything more about these particular ancestors. My Great great grandfather's name was Carmine Rossi. My great grandfather's name was Michael Rossi. Both were born in Italy. My great grandfather was born in 1861 and died in 1912. I do not know what region of Italy that they were from. Thank you in advance for any kind assistance that you can offer.