recipe.rb

include_recipe 'docker-apps'

Chef::Resource::DockerContainer.class_eval do
  property :dependencies_updated, [true, false]

  def depends_on(resource)
    subscribes :dependencies_updated, resource, :immediately
    subscribes :run, resource
  end

  action :dependencies_updated do
    new_resource.dependencies_updated true
  end

  module NewCreateAction
    def action_create
      super
      new_resource.reset_property(:dependencies_updated)
    end
  end
  # This puts NewCreateAction::action_create as the first thing called, and super() == DockerContainer::action_create
  prepend NewCreateAction
end

# And then change subscribes to depends_on in your recipe:
directory '/tmp'

file '/tmp/some_config.ini' do
  content 'blah'
  action :create
end

file '/tmp/another_config.ini' do
  content 'blah'
  action :create
end

docker_image 'alpine' do
  tag 'latest'
  action :pull_if_missing
end

docker_container 'alpine' do
  command 'sleep 3000'
  depends_on 'docker_image[some_image]'
  depends_on 'file[/tmp/some_config.ini]'
  depends_on 'file[/tmp/another_config.ini]'
  action :run
end