I've got something similar for appointments at citizens' bureaus in some European cities. The waiting time is usually around a month, which is insane imo.
My script constantly looks for open/canceled spots and reserves them (some need email/phone confirmation, which makes it a bit harder). Pretty standard stuff.
That's how I got my appointment in 3 days instead of a month.
So, I'm thinking of making money from this, but I'm not sure about the legality of it all.