This site is currently on Middleman, and the middleman-favicon-maker gem that I use to generate all the various favicon files relies on ImageMagick. My local development environment is CentOS 6.6 which, sadly, has a very outdated version of ImageMagick in yum. Thankfully, the REMI repository has an updated version, so we can get that installed very quickly.
Install REMI repository
For CentOS 6.x
wget http://rpms.famillecollet.com/enterprise/remi-release-6.rpm
rpm -Uvh remi-release-6.rpm
For CentOS 7.x
wget http://rpms.famillecollet.com/enterprise/remi-release-7.rpm
rpm -Uvh remi-release-7.rpm
Visit this resource for installing REMI on additional distros.
Enable REMI repository
Edit remi.repo (might need sudo)
vim /etc/yum.repos.d/remi.repo
In the section titled [remi] (probably the first one), change enabled=0 to enabled=1, then save and close this file.
Install latest ImageMagick
Install ImageMagick from the REMI repository (might need sudo)
yum --enablerepo=remi install ImageMagick-last
Thanks to toracat on centos.org for this