Unable to start the Phusion Passenger watchdog
First, let us make sure Watchdog is present on the system by running: find / -name PassengerWatchdog
Then if it's an RVM issue, you can try a workaround of symliking Passenger's root to the location mentioned by apache:
ln -s /home/ec2-user/.rvm/gems/ruby-1.9.2-p290/gems/passenger-3.0.11 /usr/lib/phusion-passenger
On another hand, are you sure running passenger-install-apache2-module didn't raise any errors/warnings? including its output to the question could be helpful