vagrant runs docker runs progrium/nginx

Vagrantfile

Vagrant.configure("2") do |config|
  config.vm.define "nginx" do |app|
    app.vm.provider "docker" do |d|
      d.image = "progrium/nginx"
      d.name = "nginx"
      
      # expose container ports to docker host
      # access from the vagrant host is left
      # as an exercise for the reader
      d.ports = ["4880:80","4881:9000"]
    end
  end
end

# you need rsync for this to work.
# windows users should try mingw-get.
# vagrant up --provider=docker

If you get that running you can use this to serve the container filesystem:
curl -d '{"root":"/", "autoindex":true}' localhost:4881/v1/config/http/server/0
(run it on the docker host)