Thank you, SteveH, but I went on Saturday.
Even if I went on Sunday, the 20% discount with a Conwy Card only applies to tickets pre-purchased from the Tourist Information Office in either Llandudno or Conwy and even then I would not have been allowed to use a credit or debit card to secure this valuable discount.
I guess one day I will eventually get to use this Conwy Card for the first time.
BTW, where is the Tourist Information Office in Conwy?