Have a look at CoScale for monitoring Docker. There is a SaaS version as well as an on prem version that runs on Docker. The monitoring agent itself is also containerized and can be easily integrated with your orchestration tool for deployment.
This is an interesting use case, and one I had not thought of for our CoScale platform, but it would certainly be possible. We have a lightweight server agent (with support for Ubuntu and other distros) taking minimal system resources, and you can manually select which metrics to collect such to also minimize bandwidth use.
Our agents communicates with our SaaS platform every minute, and if not online, an exponential backoff mechanism kicks in, during which data is locally buffered and resend when the connection is back available.
You can also send metrics directly to our API, or run a script or our log parsing extension on your server to send custom metrics via our agent.
Our pricing is primarily based on page views, since our main use case is web performance monitoring, but for your specific requirement we can look into custom pricing since the number of metrics you will send us is probably small.
Have a look at http://www.coscale.com if interested.