Hard to make suggestions without knowing the construction of your deck.
What may be an option is to put the railing on the outside of the screen. Carriage bolts through the rail posts, secured to the end joists would be secure, and would catch the kid if they were to fall through the screen. It wouldn't protect the screen from damage, but screens are easy to replace, and then you could simply unbolt the railings after they are old enough to remain safe.
I'm sure building code mandates that you have fall protection on a permanent basis, anyway.