Ryanair offer a Visa Card via Mbna in Ireland and they offer a Mastercard in the UK which is issued by Santander UK.
And what davidjohnson6 says is correct - If you are UK resident you will get accepted in UK for Mastercard, otherwise unlikely. Same in Ireland will only get approval for Visa if resident in Ireland.
If you change the country on the main Ryanair page and follow the link to Credit card you will be taken to the appropriate offering for the appropriate country.
Clearly Ryanair would rather people pay credit card fees rather than offer no booking fees with a Ryanair credit card.
The UK Mastercard is not a prepaid one and therefor does not allow you to avoid a booking charge!