Update: As per grawity and MonkeeSage's comments, it seems my question was pointed in the wrong direction. I've updated the title and question below...
I'm currently evaluating LXC as an option for my company to safely and easily deploy several client projects to a single virtual server hosted on Rackspace. All the articles I'm reading use Bridged networking + DHCP to give each container its own IP on the local network. Unfortunately, this isn't an option on Rackspace since they do not allow a virtual machine to allocate any additional internal IP addresses.
How can I set up my own subnet that won't conflict with Rackspaces? The containers on each server must be accessible from other hosts on the Rackspace network and must be able to access the internet.