I created tokens with each child's name on them that are good for 30 minutes of screen time. They each get two. I'll laminate them and put a magnet on the back and put them on one side of the fridge. When they use one, I'll set a timer and move one of their tokens to the other side of the fridge. There will be serious consequences for a kid that moves their own! ;)
I'm hoping this helps provide a solution to our problem. I think the kids will like it and feel a bit more in control of themselves. They usually only play for a short while before abandoning the device (still running) to head off to play. I'm hoping to also instill a habit of a central charging station where they can pick up the device from and have to drop it off when they are done. No more "where is my Kindle" when I want to read at bedtime!
Here's a printable that you can use if you'd like. Just write you children's names in and laminate (or don't). I may color mine in different colors to make it more obvious, too.