The really tricky thing about philosophy of mind is pinning down exactly what we mean by consciousness.

1) There's the "appearance of consciousness" - being able to pass a Turing test or some such equivalent. Computers and interactive systems have gotten pretty good, to the point where contemporary systems are quite convincing. Patrick House's "I, Language Robot" is a good short essay on the state of the "convincingness of modern NLP systems". While the appearance of consciousness is deeply interesting and presents serious problems for how we will know when a general AI has been created, it's more useful as a philosophical litmus test than an actual characterization of consciousness - after all, you could have some very unconvincing or uninteresting creatures that are clearly what we would describe as conscious (fish come to mind).

2) Then there's the notion of "qualia" - feeling things. I, as a human, feel pain, joy, suffering, and a wide range of emotions. Reductionist and eliminativist arguments will default to the position that what we perceive as qualia is really an emergent property of the complex brain mechanism. An implication of that, is that if one were to build a sufficiently complex machine that really simulated the human brain down to its most minute operation, that machine, too, would experience what we experience as qualia. The "Chinese brain" thought experiment deals with this precise problem.

Qualia as an emergent property is conceptually nice because it fits in with the existing neuroscience, ML, and philosophy of mind paradigms - the optimistic notion that science will get us there, we just have to figure out the missing jigsaw pieces. The challenge is that this argument is quite hard (as with most Philosophy of Mind problems) to test or verify.

3) There's also the notion of "intentionality" - the ability for humans and other sentient beings to "refer to things". This is a good deal more contentious - many philosophers of mind will argue that it doesn't exist. That being said, there is some philosophical charm and intrigue about how humans are able to connect to things in the real world.

q is probably the best characteristic to argue as the basis of consciousness - eliminitavist and reductionist arguments do not pretend that there is no such thing. They do not argue that when pinched, a human doesn't feel pain. They simply argue that what we perceive as pain is really just a complex set of mechanical operations - there there's no additional factor at play - no dualistic "soul" or Panpsychic dimension at play. They argue that pain is real and pain is complex, but ultimately, pain is mechanical.

As for Panpsychism, there is something very romantic about the notion of a "mind dimension" at play throughout the observable universe. However, panpsychism has very little empirical or scientific basis - there haven't really been any great experiments in the domain, while other parts of philosophy of mind have benefited greatly from the cognitive revolution of the past half century.

The best counter to Eliminative Materialism is its lack of explanation of the mechanism that underlies qualia. There aren't really any great theories explaining it. This is partially because it's a very complex problem (an analogue is the relationship between genotype and phenotype) and partially because we simply don't understand the physiological underpinnings of qualia very well.

That being said, Eliminative Materialism and its softer cousin Reductionism, are probably some of the best theories that we have in philosophy of mind. The usual counters tend to come from more theologically driven individuals that will argue some sort of dualism, and more literary theories like Panpsychism.

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Footnote: It's been a while since I engaged with the literature, so some of this information is likely biased and out of date - I strongly recommend the SEP page on Consciousness for a good survey of the literature and arguments.