Is there a downloadable patch that allows Pro Tools 9 to be compatible with Mac OS X 10.9.4 (Mavericks)?
No, there is no official downloadable patch that makes PT9.x compatible with OS X 10.9.x.
The official statement is that
Pro Tools 9.0 and 9.0.1 (is) not tested with 10.6.7 and higher (source: avid.force.com)
Pro Tools 11 officially supports Mac OS X 10.9 ("Mavericks"), but not officially versions >= 10.9.1. See this statement and this list of known issues (some of which you can assume applies to unchanged PT functionality in PT 9).
However several users report that it is possible to install and use PT9 on Mavericks. Simply install the latest full installer and apply eventual patches
Others experience issues such as: