I was having the same problem on a Ubuntu ec2 instance. I was following this amazon article on page 7:

Mongodb path in /etc/mongodb.conf was set to /var/lib/mongodb (primary install location and working). When I changed to /data/db (EBS volume) I was getting 'errno:13 Permission denied'.

1. First I ran sudo service mongodb stop
   .
2. Then I used ls -la to see what group & owner mongodb assigned to /var/lib/mongodb(existing path) and I changed the /data/db (new path) with chown and chgrp to match. (example: sudo chown -R mongodb:mongodb /data/db)
3. Then I updated the path in etc/mongodb.conf to /data/db and deleted the old mongo files in /var/lib/mongodb
    directory.
4. Then I ran sudo service mongodb start and waited about a minute. If you try to connect to 27017 immediately you won't be able to.
5. After a minute check /data/db (EBS volume) and mongo should have placed a journal, mongod.lock, local.ns, local.0, etc. If not try sudo service mongodb restart and check a minute later.

I just spent over a hour with this. Changing the group and deleting the old files is probably not necessary, but that's what worked for me.

This is a great video about mounting a ebs volume to ec2 instance: