Ah, that sounds good. How does Kubernetes handle updates safely? That requires pretty deep integration with the thing running in the container, doesn't it?
It supports rolling updates where one pod (this means container, usually) is updated at a time, with traffic being sent to other pods during that time.
I think the best practice right now is to use a Deployment (alternatively you can initiate a rolling update manually). Using a deployment makes updates as simple as "kubectl patch ...".
It does require a load balancer, which varies from platform to platform. In AWS, I assume it uses an ELB. On premise, you might use contrib/service-loadbalancer (haproxy).