I myself wrote:
Grub from CentOS 7 automatically created an entry for CentOS 6, but I get an error if I try to boot CentOS 6.
It turns out that Grub2 checks the version of the kernel and refuses to proceed if it thinks that the kernel is too old. I don't know how old is considered too old, but the latest centosplus kernel for CentOS 6, vmlinuz-2.6.32-754.3.5.el6.centos.plus.x86_64, apparently qualifies.
The solution was to install the latest kernel-ml kernel from ELRepo, https://elrepo.org/ , to change grub.cfg to reflect the new versions, and to change linux and initrd to linuxefi and initrdefi.
I'm surprised this has apparently never arisen before. Am I really the first person to dual-boot CentOS 6 and 7?
Thanks to Lingzhu Xiang for his bug report, https://bugzilla.redhat.com/show_bug.cgi?id=894300 , which put me on the right track.