I always read the Invoker as being the person who is infused with his or her god's essence, rather than is granted the divine power from the god. The Invoker seemed to me as the 4E version of the Favored Soul. Thus, I personally would probably see the Invoker as a Sorcerer subclass more than anything else, since the sorcerer defines "infused with magic". But rather than a draconic bloodline, you'd have a divine bloodline instead.
As I don't have the PH yet, I couldn't say what kind of adaptation of the draconic sorcerer's features you'd need to modify... but at least in terms of spells, you might be able to just use the Sorcerer's spellcasting mechanics with the Cleric's spell list.