Hi Damon,
The answer is no, there is no supported path to migrate from v6.1 to v9. Supported migration path to v9 are from v7 and 8.X
Planning to migrate product configurations
http://www.ibm.com/support/knowledgecenter/SSAW57_9.0.0/com.ibm.websphere.migration.nd.doc/ae/tmig_z_planning.html
Learn about the migration process before you migrate WebSphere® Application Server Version 7.0 or later to Version 9.0.
Knowledge Collection: Migrating to WebSphere Application Server V9.0
http://www-01.ibm.com/support/docview.wss?uid=swg27048343
You need to migrate from v6.1 to v7, v8.X (my recomendation 8.5.5) and then to v9
Knowledge Collection: Migrating to WebSphere Application Server V8.5
http://www-01.ibm.com/support/docview.wss?uid=swg27008727
Depending on your Cell topology (standalone, Cluster) and number of resources (JDBC, JMS,...) maybe you can do the migration manually, replicating configurations in new v9. I have done in several "small" clients not to v9 (yet) but to v8.5.5 ;-)
To take in mind I: you need to review all yours applications code!!!
To take in mind II: take a view to "migration help services" :-)
Knowledge Collection: Migration Offers and Support
http://www-01.ibm.com/support/docview.wss?uid=swg27013842
Hope this helps. Tell us if you need more support
Regards