There have been a few times where I have needed to migrate a VirtualBox virtual server I have built on one machine to use on another. Usually this is seamless. I simply turn off the server in question, export the appliance to a USB drive or shared folder, import the appliance, and I am all set. This works the same for CentOS 6, except every time that I have done this, the network would refuse to work. I am happy to say I finally found a solution!
After you import the appliance, go into the device settings under network (I always used a bridged adapter), and make sure the device name matches your desired setup. Click Advanced, and refresh the MAC address. Then boot up.
Once booted up, su to root and do the following:
sudo rm -f /etc/udev/rules.d/70-persistent-net.rules
Once rebooted, set your network settings, as needed, to match your network and restart the network service. In my previous attempts, this has fixed the issue.