"When I saw what [his true memory] contained, I attempted to use it to secure Morfin's release from Azkaban. Before the Ministry reached their decision, however, Morfin had died."
-- Albus Dumbledore (HBP17)
Morfin, believing until the end that he was guilty of killing the Riddles, dies in Azkaban and is buried outside the walls of the prison (HBP17).
Dumbledore says, "However, I was able to secure a visit to Morfin in the last weeks of his life, by which time I was attempting to discover as much as I could about Voldemort's past." This gives us very little to go on, but if we assume that Morfin was around 20 years old at the time of the murders and that prisoners don't live as long in Azkaban as they would otherwise, we might assume that he died around the age of 60. If so, he would have died around 1965. A less likely possibility is that Dumbledore started investigating Voldemort's past after Harry showed him the damaged diary in 1993. If that's the case, then Morfin would have been close to 90 when he died. This seems unlikely, but not impossible. For the purposes of our timeline, then, we will use 1965 as the date for Morfin's death as being a reasonable guess, but the actual date could be anywhere from 1943 to 1993.