According to a recent interview with VG247, Todd Papy, Design Director at Sony Santa Monica, mentioned that God of War III may see some paid content coming down the line after release.
Papy had this to say about completing the game, "We're gonna take a break, come back, look into new IPs, and at the same time we are going to look and see if there is anything left in the God of War series that we feel is very compelling," leaving the possibility of DLC open in the future.
There was also mention of the continuation of God of War as a franchise spanning beyond Kratos and his story.
Papy teased the possibility of a spin off by saying, "The story we set out to tell in the original God of War finishes with this one and that's, well, that's kind of where I will leave it for now."
DLC could be quite an exciting announcement to see, but it looks like it will be at least a little while before we really see it come to fruition.