How can I change the day my customer's recurring membership is billed on?

You can edit the billing day of the week or month for a customer's recurring membership.

To do this navigate to the customer's profile page.
Once here click on the Memberships tab, and select desired membership you would like to change

On the next page, click 'Edit'.

Scroll to the bottom of the page, and you will see the current billing day of the week. Click as highlighted below, to change the day/date.

For Weekly:

Click 'Submit Changes' once you have made the desired change.

For Monthly:

Click 'Submit Changes' once you have made the desired change.