A very fun solution seem... inflatable prone surfboards.
You get the small dimensions adapted to kids of a prone surfboard, with the added stability of the high volume rails, and kids love the "toy" and safe feeling of an inflatable.
Here is a 6 year old on one:
The board is a 7'5" x 23" x 3", 78 liters more specs at
www.gong-galaxy.com/magazine/pics/1-hour-4-boards/Not sold outside of France, but maybe you can find something similar locally, or a beginner foam surfboard or with a foam deck.