Tried to pay my City National Bank Crystal Visa Infinite last night around 9 pm ET with "Visa" biller for $1.88. It gave some error message about not being able to accept the biller because payment wouldn't be delivered until the following business day. Anyways, tried again this morning and it gave the same message (CSR last night theorized it was past the cutoff time and might work in the morning). So CNB CCs seem to be a no-go. Also tried paying "City National Bank" $1 for 3 day delivery and it didn't work either. That biller was in North Carolina though so I'm thinking it may have been
the "other" CNB.
tl;dr There doesn't seem to be a way to pay City National Bank CCs with CheckFreePay.