There is currently no way of obtaining the PaymentDate-field from a CustomerPayment-object via the API.
When we look at the list of CustomerPayments (AR3020PL) we see:
When working with Financial, many users consider this field when the Payment has "happened", from VNs point of view. The field is the DocDate that we can also see in the Financial Details-tab (AR302000) for a CustomerPayment:
This seems to me to be a fairly important field. For example when reporting Payment-data to a different system we need to know which date the Payment is from, since it affects CustomerBalance. And we cannot rely on/enforce Financials-users to always set the same ApplicationDate, because they will not.