Docker has announced the release of Docker 0.11 http://blog.docker.io/2014/05/docker-0-11-release-candidate-for-1-0/ Of particular interest is the seLinux support (thanks to Dan Walsh) There is already a build for Fedora 20 but not EPEL 6/7
It is in the works. Thanks for the report http://koji.fedoraproject.org/koji/packageinfo?packageID=17053
there's a pull request for el6 here: https://github.com/lsm5/docker-io/pull/8, but it looks like there's trouble getting docker to run with lxc or libcontainer.
docker-io-0.11.1-4.el6 has been submitted as an update for Fedora EPEL 6. https://admin.fedoraproject.org/updates/docker-io-0.11.1-4.el6
Package docker-io-0.11.1-4.el6: * should fix your issue, * was pushed to the Fedora EPEL 6 testing repository, * should be available at your local mirror within two days. Update it with: # su -c 'yum update --enablerepo=epel-testing docker-io-0.11.1-4.el6' as soon as you are able to. Please go to the following url: https://admin.fedoraproject.org/updates/FEDORA-EPEL-2014-1419/docker-io-0.11.1-4.el6 then log in and leave karma (feedback).
docker-io-0.11.1-4.el6 has been pushed to the Fedora EPEL 6 stable repository. If problems still persist, please make note of it in this bug report.