Both of these services may provide access to certain Supreme Court filings. Simply navigate to the case you're looking for and then click the filings tab.
Proquest:
Proquest also has access to some Supreme Court filings and other related documents. Try searching by case name or full citation.
Audio Recordings (2010–present) - The audio recordings of oral arguments heard by the Supreme Court of the United States are available to the public at the end of each argument week.
Print Transcripts (1968–present) - Print transcripts are posted to the website on a continual basis.
The Oyez Project - Cornell’s Legal Information Institute (LII), Justia, and Chicago-Kent College of Law have created a multimedia archive of the Supreme Court of the United States. Oyez offers transcript-synchronized and searchable audio.