Alternative to Kubernetes rolling update in rest api
I think the Kubernetes Deployment object is what you are looking for. It is an object in the Kubernetes REST API (as opposed to the client-side magic in kubectl rolling-update).
You can specify .spec.strategy.type==RollingUpdate as your Deployment Strategy to get similar behavior to kubectl rolling-update
If kubernetes is not strict requirements and you can switch to latest openshift origin (which is "kubernetes on steroids") you can use origin feature called "deployment". Openshift deployments are accessible via api similar to general kubernetes api.