For all groups teen and younger... (anyone not an adult) You should have at least 2 "leaders" (coaches) at all times. I would take a look at the Scouting Youth Protection system, two deep leadership stuff for some good ideas. The basic idea is to make sure there is A) no one on one contact between adults and kids and B) no appearance of one on one contact. You always want other people to support your story of what did or did not happen.
The Scouting program will go a little overkill, they want one leader per kid for their youngest (1st grade level). That's probably a little much. But you will want as many eyes around as possible, the younger the kids are. Even if they are not out on the mat. I would encourage the parents to stay and watch their kids.... it is as much to protect you as it is to protect their kids. If any kind of accusation is made... you want as many witnesses as you can get saying it did not happen like that.
The Scouting program gets into tons of details about things like digital communication, phone calls, private conversations, cameras.... These are things to at least think about. If you have minors of any age, include a parent on every email and text sent, make sure there are people around if you are on the phone with a minor, never be alone with a minor.
I have seen way to many martial arts instructors ignore these types of things. They send an email to all the students "testing is next week, remember to wear your best uniform," then one student replies just to the instructor "am I testing?" Instructor replies "yes, wear your best uniform," student "do you think my blue one is the best?" Instructor "yes you blue one is fine" Now the student fails the test... "But the instructor told me how much he likes me wearing my blue gi and how good I look in it... so I wore it for him and he didn't pass me, watch out for that creep...." And we have all seen the stories wear the instructor is a creep.
I know you were looking for people on the mat helping them to stay on target with the class.... But, I wanted to at least throw this out as well.... consider protection and witnesses for both the kids and the coaches.... everyone can get burned here.