A BigTable table can be backed up through GCP for up to 30 days. (https://cloud.google.com/bigtable/docs/backups)
Is it possible to have a custom automatic backup policy?
i.e. trigger automatic backups every X days & keep up to 3 copies at a time.
As mentioned in the comment, the link provides a solution which involves the use of the following GCP Products:
Cloud Scheduler: trigger tasks with a cron-based schedule
Cloud Pub/Sub: pass the message request from Cloud Scheduler to Cloud Functions
Cloud Functions: initiate an operation for creating a Cloud Bigtable backup
Cloud Logging and Monitoring (optional).
Full guide can also be seen on GitHub.
This is a good solution since you have a certain requirement that should be done with client libraries, because Big Table doesn't have an API that sets 3 copies at a time.
For normal use cases however, such as triggering automatic backups every X days, there's another solution such as calling the backups.create directly by creating a Cloud Scheduler with HTTP similar to what's done in this answer.