During the interaction, especially at points where they start resisting the price, say you can finance it for 12 months, no interest. After you sell them on the financing, break it to them that it's via the credit card, but soften the informing by mentioning its usually a quick process and its a soft credit check -- doesn't ding your credit for checking. It's also free for most people.

If you mention that it's a credit card upfront, their mind shuts off and they immediately go on "no, no, no" mode. As long as you really don't procrastinate mentioning it for too long, I don't see it as unethical. The words "credit card" shut people off before they even consider what it can do.

Also, never bring up financing at the end of a sale. Like someone else mentioned, they've already figured out payment by then.