How many tennis racquets are there in the US?

Unfortunately, there is no way of obtaining this number, because not all clubs, private or public, are registered or otherwise listed, publicly. Furthermore, not all clubs having tennis courts designate themselves as such (i.e., they may be named as a "Golf club" or "swim club", etc), and a "private tennis court" could also be construed as a personal/residential tennis court, which do not have any members other than the immediate family.