Payroll subscriptions are not required, Courtney. Your client can still submit the Employer Payment Summary (EPS) without subscribing to payroll.
Since your client is registered as a CIS contractor with no employees, they are not required to submit Full Payment Submissions (FPS), which are used to report employee pay and deductions. Instead, they need to submit an EPS each month to report the CIS deductions suffered, that is, the tax deducted from subcontractors’ payments that the client pays to HMRC.
You can advise your client if they want to submit an EPS directly to HMRC without having a payroll subscription or running full payroll. Especially since they don't have any employees to pay, they can contact HMRC directly for guidance on how to process and submit the EPS.
However, if they want to record the CIS deductions suffered using a payroll subscription, you can provide this article to your client for more information: Record CIS deductions suffered in QuickBooks Online Core Payroll.
You can revisit this thread if you have additional questions.