The Diamond featured in GTA IV never originally belonged to anyone, but the most appropriate known origin is when the Cook steals it from Ray Bulgarin, though the diamond changed hands from person to person including Niko Bellic, Johnny Klebitz and Luis Fernando Lopez.
The myth involving the diamond isn't the history of the men who stole it, but in fact it's the origin and the fate the of holder of the diamond. Any person that possessed this diamond was killed in some way or another. These deaths include Evan Moss, Joseph DiLeo, John Barbosa, Luca Silvestri, Mori Green, Isaac Roth, The Cook, Bulgarin's henchman, who throws them onto a truck, Ray Boccino, Johnny Klebitz, and Ray Bulgarin. However, three specific people were never murdered, being Niko Bellic, Luis Fernando Lopez and Jerry Kapowitz.
The current owner of the diamond is unknown after Jerry Kapowitz sold them, most probably in the black market. Some have theorized that this diamond is still in Liberty City's black market, but this is still not known, as the mysterious possession of the diamond remains unknown.
The diamond could be a reference to the Hope Diamond. The fact that every owner died in some way connects the GTA IV diamond to the real life one.