I just checked the Black Card FAQ and either I'm blind or the information is not covered there, but there is more info about the multipliers in the Black Card Rules section.
It is also the only logical thing, since all multipliers calculate bonus FTP's from your base FTP's.
So, Black Card doubles (or triples) your base FTP points. And Happy Hour doubles your base FTP points. So it's 3x FTP's with 2nd BC tier + Happy hour or 4x FTP's with 3rd BC tier + Happy hour.