I would make it part of the instructors procedure to have class attendees sign into class. A simple clip board and pen are all it takes. If you have interns working at your club, they can do the tallying. If you want the instructors to do it, you will need to pay them a little extra. If you do it, do it everyday or it will become overwhelming. Though if you number the sign in sheet, you only need to look at the number of the last person to sign in.
There are other ways to do it. Card swipe systems, front desk check in, etc.
At one of the gyms I work, they implemented a ticket system about a month ago. Members have to sign in on a clipboard, check off whether they’re a pass-holder (2 levels) or a drop-in, and they also have to sign in at the front desk to get a ticket (room capacity reasons). I’m supposed to take the tickets while people are signing in, and make sure the # of sign-ins matches the # of tickets.
My class is a small yoga class in a little yoga room. I only have to manage 10 to 15 sign-ins. It’s a pain in the butt. However, we do it because our class funding depends on attendance. I can only imagine how much of a pain it is in the large studio where the big weekend classes are held.