I needed a newer version of ImageMagick than is available on the yum packages on Amazon Linux. I tried using the remi repo but it failed with dependency errors. Here is what I did to install ImageMagick with support for PNG, JPG, and TIFF.
download the most recent package
uncomress the package
tar -vxf ImageMagick.tar.gz
install the devel packages for png, jpg, tiff. these are dependencies of ImageMagick
sudo yum -y install libpng-devel libjpeg-devel libtiff-devel
configure ImageMagick without X11. this is a server without a display (headless) so we don't need X11
cd ImageMagick ./configure --without-x make && make install