I have a set-up running on Amazon cloud with a couple of EC2 Instances running through a load balancer.
It is important that the site has a unique(static) IP or set
Really the only way I am aware of doing this is by setting up your instances within a VPC and having dedicated NAT instances by which all outbound traffic is routed.
Here is a link to the AWS documentation on how to set up NAT instances:
http://docs.amazonwebservices.com/AmazonVPC/latest/UserGuide/VPC_NAT_Instance.html