They offer several payment methods, one of them being a credit card.
They offer several payment methods, one of them being the credit card.
They offer several payment methods, one of them being credit card.
Technically, all three could work. The item is going to be a "payment method". Thus, your parenthethical-- what's separated from the rest of the sentence-- is going to talk about one of the options. So, there is nothing wrong with saying a, the, or an omission. I will say, however, that the a sounds the best because you are talking about a single method. But the works in the way that you are talking about the credit card as general method, not a single item from that class. With the omitted article, you are getting a little sticky. It doesn't really flow off of the tongue as well as the other options, but is it wrong? I say not. When you say it aloud, it simply sounds like you are, again, talking about a general option of payment. It would work the same way if you exchanged "credit card" for "cash" or something of the sort.