Can you purchase a cashier’s check or money order using a credit card?

Most banks won't do this, because you have the option of doing a chargeback on the transaction. However, you can pay with a Debit card, which banks will allow.

Banks will usually not allow for Cashier's Checks and/or Money Orders to be made with financial instruments that can be used to do reversal of charges and hence be subjected to possible fraud vulnerabilities.