I don't believe this is a feature, as a workaround though you could setup something to interact with the API to enable and disable your synthetic at certain dates/times.
Details on the API for editing a synthetic can be found here:
We have a API that exposes the frequency of monitors can check on the same. However if my understanding is correct you can even try the built-in outage handling & alerting? (Monitor settings -> Outage handling) which will help to implement own alert handling. Currently this may not be supported if you want to extract a metric to pin it to dashboard.
For scheduling monitors at specific times of day or days of the week, we recommend the use of Maintenance Windows. One of the options when creating a Maintenance Window is to disable Synthetic Monitors . So you could do this for groups of monitors or single ones to get them only running at specified times.
Just letting you know that there is a new API allowing for manual triggering of a batch of synthetics so you can create a tool that targets that API. Alternatively you can also manually trigger a synthetic at any time within the UI but still cannot schedule it for any time within the UI.
Docs for triggering synthetics with the API can be found below: