Is it permissible to obligate students to pay private tuition fees on a specific day of the month, regardless of the number of classes they attended?

As long as you dedicate yourself to giving lessons at the agreed-upon times between you and the students, you are not accountable for their absence from them. You are entitled to the fees for those lessons from them, whether they attended or not. There is no harm in setting a general deadline for paying the fees, regardless of the actual number of lessons the student attended.