With the exception of the obvious thematic premise of the mother and daughter dynamic in Toni Morrison's Beloved, outside of Kristeva, how can deconstructionist literary criticism be applied to specific passages in Beloved in a graduate level research paper?
It is in the close textual analysis of individual passages that deconstructive literary criticism, especially as practiced in the anglosphere, is closest to New Criticism as a practice, despite the fact that many of the original deconstructive literary critics who practiced close reading often consider themselves as rebelling against New Criticism.
The way to apply deconstructive criticism to a passage (it works for any practice chosen at random) is to address the thematic concerns of deconstructive theory. The most typical deconstructive move is to look for binary oppositions, especially binary where one side of the opposition is valorized by society. For example, one could look at black/white, good/evil, sane/insane, or male/female. In the case of each binary, one can show first how each side of the binary depends on its opposite for its existence. Next, one can show how Morrison subverts the binary opposition by either reversing the implicit hierarchy or erasing the opposition.
Another strategy for applying deconstructive criticism to Beloved would be to use the notion of the trace, and show how the present of the text is dominated by things which are absent.
One passage that would be particularly interesting for deconstructive analysis would be the story of the rapists drinking Sethe's milk, as it evokes the oppositions between adult/baby, conventional motherhood/rape, black female fecundity/white male lack, etc.