Since shinyapps.io is designed to be an auto-renewing and entirely self-service platform, there's not a simple way to change the billing date. If you wish to change the payment date, you would need to cancel your current plan and then subscribe again on the date you want to have your new payment cycle begin.
However, it's important to note that if you choose to cancel at any point in your current billing cycle, the unused time that has been paid will be forfeited. This is documented in the user guide:
Please note that at this time cancellations take effect immediately and the entitlements in the subscription cycle do not continue until the end of the subscription cycle. In addition, there are no partial refunds.)
Canceling to return to the free level plan to make the switch may also cause an inconvenience, as you will need to revert all account settings to the free level to downgrade.
- Archive all but 5 applications
- Archive, or make public, any private applications
- Reduce the size of your Application Instances to Large or smaller
- Remove all additional users from the Account (Pro only)