We had the same dilemma and wanted something that wouldn't make the deck darker or change the look of it too much. My bright idea was to buy rolls of the stuff that is used as flyscreen on security doors. This stuff is strong like a thick wire mesh, doesn't go brittle from the sun and doesn't fall apart like the string type stuff.
It was attached using a builders staple gun and is definitely strong enough to hold the weight if a child fell against it. Of course I wouldn't leave her completely unsupervised or anything but she has never tried to climb or break the stuff in any way. Was relatively cheap..I think the rolls were about $30 each from Mitre10 Mega, plus the cost of the staple gun and galvanised staples.
This is a photo when we had done most of the deck, just hadn't done the gates at the time (but that is completed now too).. Totally worth it and no more stress about Alyssa falling through the gaps!