This is a great question, unfortunately, Recurly does not currently offer the ability to record payments in advanced for subscriptions. This is something that our product team is tracking interest in, please feel free to reach out to our support team directly if you'd like to be added to our mailing list. There is a workaround that we advise which may help you achieve this within your own use case scenario.
You can issue one-time charges and invoices to a customer's account whenever they would like to make an advanced payment towards the subscription. Once that invoice has been collected as paid, you can then issue an open credit adjustment on the account. This credit can be left on the account as an exhaustible amount and will be used to discount the next invoice billed to the customer from their subscription.