discount with advance payment

I am entering this as a comment because others might have some ideas, too.

You could accept the payment and leave it as a credit in the customer's account.  Then when you created an invoice you would pay using the credit.  Until the credit was used.  You could have some indicator flag to show that the customer got the discount.

Then you could have two items for every service - one for regular service with the regular price and one for the discount price.  For the customer who are flagged as paying a deposit, you would use the discounted item on your invoice.  For regular customers you would use the regular items.