A few years back I knew a couple of companies that offered software designed to meet the M.A. school needs, including card scanner interfaces for automatic attendance tracking. They probably now offer Web-based versions.
You may also want to look at searching “gym/fitness club software” etc.
The software product I selected for my school believe it or not was a “church management software” program. It was cheaper than the commercial martial arts software at the time, their interface was built over an underlying Access database. I was amused for I never knew doing the Lord’s work was so financial.
However as Nolerama has inferred - it may simply come down to a cost-benefit analysis of doing something homegrown.
I mean how many students/how much activity are you really tracking? Any software will require a learning curve and admin. set-up time, so the KISS method may be best.
Check out MainStack MainStack Simple Martial Arts Billing Software It's the simplest software we've used and performs all the things most schools need. Our students type their names in when they come in, but it also does barcode scanning if you're into that.