With CentOS 6 everthing is handled by udev now. Go into /etc/udev/rules.d and delete the 70-persistent-net.rules file and reboot. If you open it berfore hand you will most likey see the original NIC MAC listed as eth0 and the new one as eth1.
Deleting the file forces the detection process to run again at boot with no baggage left over from the cloning process, namely the old NIC MAC address(es).
I have to do it with my CentOS 6 clones on VMware ESXi 4.1 all the time. It’s a pain kudzu would just handle it in the past with previous versions.
You will also need to remove the MAC addresses from the NICs too, in /etc/sysconfig/network-scripts/ifcfg-eth0 etc.