Well, the only "continuing characters" from GF III who would, presumably, appear in GF IV would be:

Michael Corleone - Al Pacino
Connie Corleone - Talia Shire
Kay Adams-Corleone-Whatshisname - Diane Keaton
Vincent Corleone - Andy Garcia
Anthony Corleone - Franc D'Ambrosio
Al Neri - Richard Bright


Minor characters:
Enzo The Baker - Gabrielle Torrei
Johnny Fontane - Al Martino
Grace Madison - Bridget Fonda
Dominic Abbandando - Don Novello
Andrew Hagen - John Savage


Out of the "major" characters, Pacino, Shire and Keaton are all still hale and healthy. I haven't seen Bright in anything in a couple years but Al Neri's role would certainly be that of a very "senior consigliere" at this point.

Torrei and Martino, I'm not sure about, but it wouldnt be a GF film without Enzo and Johnny, would it? I could see Johnny Fontane's glitzy Las Vegas funeral being the set-piece for one of the early plot points - maybe the first business meeting of the long-absent cousins Santino Jr., and Michael Francis (Rizzi) Corleone, with Anthony and Don Vincent Corleone. (Maybe they could reopen the Lake Tahoe house as a set...)

In the grand GF tradition of abruptly writing people out of the story line, I don't think anyone would object in the least if it was explained that shortly after Mary's murder, Vincent became suspicious that B.J. Harrison had supplied Lucchesi and Altobello with info which helped set up the attack at the opera house - and shortly thereafter, B.J. went on a fishing trip with Al Neri.

And by the mid-to-late 90s - the time frame for my version of GF IV - it's entirely reasonable to believe that Andrew Hagen would have left the priesthood and gone to work for the Corleone organization.

I'll just tick off a few plot points I think would logically follow in the "coda" sequences:

1) Immediately after Mary's murder, Michael withdraws from active involvement with the family for a period of maybe 10 years. Michael retires to Sicily where his overall health improves. Connie, with her eye for manipulation, remains more directly involved in the family as Vincent's ultimate consiglera.

Vincent marries Grace Madison a year or so after Mary's death, and they have a son, Vito Pietro Corleone, and daughter, Carmella Luciana Corleone, in the early 1980s (1981-1983).

In the early 1990s, underworld manipulation and infighting leave Vincent in a position where he has to ask Michael for help. "Once he thinks he's out, they pull him back in."

2) The shock of seeing Mary's murder fundamentally unhinges both Kay and Anthony. At first, they cut off all contact with Michael, but they remain embittered and enraged which grows worse over the years.

Anthony's opera career stalls and he returns to law practice, where he becomes wildly succesful for defending several high-profile celebrity clients from drug, murder and sex-crime raps. (They are all guilty, we are led to believe, but Anthony gets them off.)

Finally Kay advises Anthony that the only way he - they - can get revenge for Mary's death, is for Anthony to join the family operation. Michael at first disagrees, but Vincent and Connie see that Anthony's smoothness and legal skill would be useful.

3) Connie's son Michael Francis (Rizzi) Corleone finishes a decade-long federal prison drug trafficking sentence in the late 1980s. He is almost 40.(We also find out that his brother Victor, who was married with a son, was killed in a stolen-car crash in the mid-1970s.) He now wants into the organization.

4) At the same time, Santino Jr. - who has been living quietly as a real estate developer in Florida, is wiped out in a stock fraud case which results in his indictment. He is in his mid-40s. He is convicted and gets a suspended sentence, but also decides it is time for HIM to get involved in the family business, which his "bastard" half-brother Vincent is now in control of.

Santino also has a son, Mario Corleone, who was born in the late 70s when he and his ex-wife were living in Miami, and another son, Giorgio Corleone, about the same age as Vincent's kids (b. 1981). Connie's grandson Victor (Rizzi) Corleone Jr. (b. 1972) also went to live with his uncle Santino in the 70s, when his dad was killed in the car crash, and mother died of a drug OD.

Well anyway, that's how I'd do it for starters...

(and set up GF V and VI while we're at it too... )