We've employed a token reward system that determines screen time. Earning 4 tokens = a show or 20 min of gaming time. 8 tokens = a movie or documentary. 12 tokens can be used for a special outing (bouncy house, carousel etc.) or playdate. Of course, you could customize token numbers/time limits.
We give tokens for positive behaviors (no taking away tokens, as they are only positive reinforcement).
This system has worked really well for us. Also, a good way to get yourself to focus on positive behaviors. It helps build a child's executive function (delaying gratification). And it's not up to you as a parent to limit the screen time, it gives the control over to the child to earn and save up for screen time.
