Daily parking at BART can be paid via Clipper Card but you have to set up an EZ-Rider account. See http://www.bart.gov/guide/parking/index.aspx and the section on Daily Fee Parking.

Airport Parking is payable via credit card and must be paid for in advance of arrival at the BART station where it will be used. When you pay for it, you'll print out a parking permit displayed on your dash.