Credit Cards in Ireland

The Capital One benefit is for you, the cardholder, not the merchant. The merchant's processing service contracts would be a flat rate for any Visa, any MC, any AmEx, etc, which is the middle-man of the operation. Some businesses just won't be set up to accept credit cards at all, or some won't have a contract that includes AmEx.

Some small hotels will not take credit cards, some will add 3% transaction fee for credit cards or conversely give 3% discount for cash, some would prefer cash but will take cards. Large hotels don't care.
American Express is least popular, as they charge a higher fee and pay slower than MC or Visa.
I talked with Uwe at Pension Peters in Berlin. He said he get's charged 2.5% from MC and Visa, so he charges 3% for credit cards, and complains that he doesn't get paid for 15 days (while it will post to your card account immediately). He won't touch American Express.
Small hotels are usually family owned, are less expensive, the owner or family member handles the money, so it is a better deal for both of you. A large chain hotel actually prefers credit cards. Limits the amount of cash that employees handle and they charge enough that the credit card fees are inconsequential.

And yes, many credit card issuers will tack 3% on to YOU for "foreign currency" conversion fees. Capital One and a few others do not.

Medium to large hotels in Ireland will take most American credit cards, including Amex. Some B&Bs won't take any credit cards whatsoever, because of the fees associated with them.

As Laura wrote, it's unlikely they'd treat a Capital One card any different from a Visa or MasterCard. My advice is to carry your normal credit card, check in with the places you are going to stay so you know in advance, and carry cash. Frankly, cash is cheaper for everyone (and this comes from someone who loves to pay with his credit card for the points).

Capital One is a bank. It issues Visas and Mastercards. So, you won't see "Capital One" as a type of credit card in a drop-down listing, any more than you would see Citibank, Barclays, Banque de France, or any other bank. It's the Visa or Mastercard that determines whether or not the B&B will take it. If they take, for instance, Visa, they will take a Capital One Visa like any other. As you have said, it's to your advantage to use a card (like Capital One or many credit union cards) that does not assess fees on your end; but as Laura said, the fees to the merchant (in this case the B&B) are a different issue. Call the cards you currently have and see what the fees for foreign use are; you can then decide if you want to get another one.

Similarly, if you are paying cash, it's to your advantage to get it from an ATM using a debit card with the lowest possible fees. Good sources of such debit cards are credit unions, Charles Schwab, and TD Bank, among others. Bad cards to use are from the likes of Chase and Bank of America, which can charge as much as 3% of the transaction plus $5 for every ATM withdrawal. Call your current banks to see what their fees are for foreign ATM use.

Much more great money advice if you follow all the links on Rick's money page: http://www.ricksteves.com/travel-tips/money