In fact, the only powerful pro-animal rights argument I am aware of is the aptly-named "marginal humans" argument. This argument can be summarized as follows: Some humans (brain-damaged, comatose, senile, infants, small children, etc.) do not have the capacity to make/grasp/apply moral law AND/OR make propositional claims AND/OR reason, just like animals; therefore, marginal humans and animals enjoy the same "rights" status, which means that marginal humans and animals either have no rights or full human rights. I admit this argument is difficult to refute in a non-consequentialist manner.
Carl Cohen, a professor at the University of Michigan Medical School, offered a principled deontological objection to the "marginal humans" argument in a 1986 essay published in The New England Journal of Medicine. Cohen claims that the "marginal-humans" argument is a false argument because "it mistakenly treats an essential feature of humanity as though it were a screen for sorting humans", any "capacity for moral judgment that distinguishes humans from animals is not a test to be administered to human beings one by one", and humans "who are unable ... to perform the full moral functions natural to human beings are certainly not for that reason ejected from the moral community." Ultimately, Cohen asserts that "rights" are a trait of species, not of individual animals. Hmmm. Cohen's "species" argument is, at first taste, difficult for a plumbline libertarian to swallow due to its collectivist nature. But does the collectivist orientation of Cohen's argument, by itself, eliminate it from libertarian consideration? I don't know, so I shall research and reflect then report my conclusions to the readers of the LIBERTARIAN BIOETHICS BLOG.