I'm running into some roadblocks:

Vito Corleone: The Racetrack Tout (Sheldon Leonard)
Sonny Corleone: ???
Fredo Corleone: Barney Fife (New York scenes) and Ralph Furley (Nevada scenes)
Michael Corleone: Keith Partridge
Tom Hagen: Arthur Dietrich
Johnny Fontane: ??? (Robert Goulet, as himself?)

Tessio: Phil Fish
Clemenza: Norm Peterson
Luca Brasi: ???
Pauly Gatto: ???
Willie Cicci: Cosmo Kramer

Mama Corleone: Thelma Harper (if she can handle the accent)
Kay Adams: Laura Petrie
Connie Corleone Rizzi: Rhoda Morgenstern
Lucy Mancini: Carla Tortelli
Carlo Rizzi: ???
Apollonia Vitelli Corleone: ???

Capt. McCluskey: Sgt. Morgan O'Rouke
Virgil Sollozzo: ???
Barzini: ???
Jack Woltz: Martin Crane
Moe Green:

I think Fish from Barney Miller (Abe Vigoda) would be perfect for the role of Sal.

I think Fish from Barney Miller (Abe Vigoda) would be perfect for the role of Sal.

Yes, that's Tessio.

Where does Tony Soprano fit in? He has to be in there somewhere!

Where does Tony Soprano fit in? He has to be in there somewhere!

The Sopranos was a sitcom?

The Sopranos was a sitcom?

Steve van Zandt (Silvio) had a gangster comedy called Lilyhammer. His character from that, Frank Tagliano, could maybe be Tattaglia or one of the other bosses.