Caveat about grad students giving practice assessments: um, they're practice assessments.
When I was in grad school, I did not give any of my practice examinees formal results, on the grounds that my lack of clinical (or even technical) fluency made the results low in validity. I reported (other than to my professors) only in terms of general categories, and never on paper.
What you are looking for, actually, is post-doctoral fellows doing their year of APA-required clinical internship in an on-campus clinic. Cheaper than a board-certified psych, definitely under the supervision of a licensed psych, and likely to be more skilled than a pre-doctoral grad student.
If you do look for grad programs, you'll be looking for clinical psych, counseling psych, ed psych, school psych, neuropsych (often a post-doc cert). Some schools they may be housed in include psych, education, child/human development.
