Could there be zombies that believe they are conscious?  They have no consciousness, but they erroneously believe that they do. That may seem possible if we think of their beliefs as implanted at birth or something of the sort: couldn’t a super scientist simply interfere with their brain to install the belief that they are conscious, as innate beliefs are installed by the genes? The belief is false, but that is no obstacle to belief possession. We may have an innate belief that we are surrounded by a world of external physical objects, but that belief might be false if we are really brains in vats. Similarly, zombies might have false beliefs about their mental world, supposing it much fuller than it really is.
But the matter is not so simple: for beliefs need reasons. What reason could the zombies have for believing they are conscious? The reason we believe we are conscious is that we are conscious and this fact is evident to us–without that we would not have the belief in question. If the believing zombies were to reflect on the beliefs they find implanted in them, they would wonder what grounds those beliefs—what evidence there is for them. Finding nothing they would abandon their groundless beliefs, perhaps with a shake of the head at being so irrationally committed to something for which they have absolutely no reason. Minimal rationality would quickly disabuse them of their error; they would believe instead that they are not conscious, or possibly remain agnostic.
It might be replied that consciousness is not necessary to ground belief in consciousness, only the appearance of consciousness is. The zombies have to be in an epistemic state just like our epistemic state except that we have consciousness and they have none—the appearance of consciousness without the reality. But this is contradictory, since the appearance of consciousness would have to be a form of consciousness: it would have to seem to them that they were conscious. For instance, it would have to seem to them that they have a conscious visual experience of yellow without having any conscious visual experience (of yellow or anything else). Surely that is impossible: seeming to have a conscious state is having a conscious state (of seeming). So the only reason they could have for believing they are conscious is that they are conscious, and they need a reason for that belief if they are to have it stably.
Now it may be said that we are being too rationalistic about belief: people can believe things for no reason at all, without any evidence whatever. Couldn’t our zombies believe they are conscious because this is what they have always been taught or because of superstition or from wishful thinking? They want badly to believe they are conscious (it seems so undignified to be a mere zombie) and so they deceive themselves into believing it. Happens all the time: no evidence at all, but firm belief nonetheless. That sounds like a logical possibility, though it would be an odd case of irrational dogma or motivated self-deception. One problem is that irrational believers generally think they have reasons for belief, even though these putative reasons look hollow and unconvincing to everyone else. They will cite these reasons when challenged to defend their beliefs. But what will the zombies say when challenged? They can’t point to anything that even appears to look like consciousness, since that would imply that they have consciousness. People whose religion requires them to believe in miracles will cite certain natural events as proof of said miracles, however unconvincing these events may be as evidence of miracles; but our zombies have absolutely nothing to point to, since the mere semblance of consciousness is a case of consciousness. Their religion may require them to believe they are conscious, but they can point to nothing that could even be interpreted as consciousness, because they have no consciousness. An appearance of miracle may fail to be a miracle, but an appearance of consciousness is always consciousness. And nothing else could provide any halfway reasonable grounds for their belief. So we are left with the idea that they believe they are conscious without even believing they have any grounds for that belief.  This gets us back to the case of beliefs that exist without even having any purported justification. All they can say when challenged is, “I simply believe it”. This is a difficult thing to make sense of because beliefs need grounds of some sort (they purport to be knowledge after all).
We should conclude that zombies that believe they are conscious are not possible. Any being that believes it is conscious must be conscious. That includes us: if we believe we are conscious, then we must be conscious. This refutes an eliminative view of experiential consciousness: it cannot be that we lack such consciousness while simultaneously believing that we have it. We cannot be actual zombies under the illusion that we possess consciousness. 
 These are zombies with respect to experiential consciousness not zombies tout court, since they are stipulated to have beliefs. The intuitive idea is that they have no conscious experience and yet they believe that they do: for example, they think they have conscious visual experiences of colors, but they don’t have any such experiences.
 They may have a sacred text in which it is written that zombies are conscious, despite the introspective appearances, and they may be brainwashed into accepting that text. But then the “belief” they have is really a matter of faith, since they have no direct grounds for the belief, even of the thinnest kind. They accept the text only because of their religion, not because they can offer any justification for the beliefs it recommends. They don’t really believe they are conscious, as they (rightly) believe themselves to be embodied believers. For that they need some sort evidence, even if it falls far short of what it is evidence for.
 Some extremists have sought to deny that “visual qualia” (etc) exist, despite our firm conviction that they do exist. But it is simply not possible to believe in such things without there being such things, since they provide the only possible grounds for such a belief.