While we don't yet know the cause of death, we can put a date on his death, thanks to his headstone. Also, at one point, while Joanie is cleaning up the house, she throws out a tray full of medications, leading us to conclude Cole died after a long illness.
Considering the history of depression on his side of the family, and how emotionally distraught Cole seemed for much of Season 4, it definitely wouldn't have surprised us if Cole had met his end much sooner. But it turns out Cherry was right that her son takes after his mom, not his dad. It seems he lived to be 74 years old and was probably alive to become a grandfather to Joanie's daughter, Madeline.