I take a three prong approach to this...
1. Alleviate anxiety. Beginner falls are mainly backwards and resemble a slow slide into home. So, if you fall, just gently slide into home.
2. Getting up - almost impossible to teach on flat bunny slope. Add zero upper body / core / lower body strength and limited coordination - errrrr just take off your skis. Just make sure they put their skis back on the right feet. (Just kidding I get this question constantly)
3. DON'T FALL in the first place. Does Superman ever fall out of the sky? NO. Why? Because his hands are out in front of him and he is leaning forward. So, if you feel like you are falling backwards, cowboy up and do your best superman impression. Superman saves the day. Superman is brave. Superman flies TOWARDS danger. Be like superman. Lets practice - everyone in line show me your best superman impression. Just make sure there is a clear runout area for superman to slowly decelerate.
Another gem is "Losing your cool while falling back? DO NOT roll down the windows! DO dive in the pool." Of course no one under the age of 30 know what the hell it means to roll down a window.
Once you can get your banana peel fallers to follow this Superman strategy, you will do a LOT less picking up pieces.
One last thing for pros - DO NOT let clients try to grab you to stay up or get up. Keep your DISTANCE. Then I give a short terse speech : "Please do NOT grab me or pull on my hand until I say. When I am ready I will count down 1-2-3 UP. Do you understand?" Only then will I offer a hand after I have my feet set and am in a good stance. You do this for a living. BillyBob who has 100#s on you jerking you around as he lumbers to his feet = tweaked back or knee. Work Smarter not Harder.
DISCLAIMER - I have no idea how to alleviate the well deserved anxiety and excruciating agony of falling on a snowboard. Maybe suggest wearing hockey pads?