From the page http://jdbc.postgresql.org/download.html:

If you are using the 1.6 then you should use the JDBC4 version. If you are using 1.7 or 1.8 then you should use the JDBC41 version.

Hence JIRA 6.x Java 7 is supported, but we still ship with PostgreSQL 9.0 JDBC4 (build 801)

Workaround

Download the JDBC41 driver from http://jdbc.postgresql.org/download.html and replace the existing postgreSQL driver in $JIRA_INSTALL/lib with it.