I know it's a total redneck solution but I want to rainproof under the
deck and improve traction on the shady mossy slippery surface on the
deck. There is no frost here... mild climate.

If I use 6 mil black plastic liner and a staple gun will that work? I
guess I'd tape the seams of the plastic liner but maybe it'd still drip
through the staple holes. Doesn't need to be perfect. Rubber liner
sounds expensive. Actually the nicer quality fake lawn at Lowes is
$4.46/SF & would cost $700 but maybe I can find a better price somewhere
or it's just a stupid idea I should forget.

Outdoor carpeting for boats is applied with double sided tape or glue
but that won't work with the liner below and would be a permanent mess.
Normal carpet is applied with those deadly looking spiky strips but I'm
not sure that works with this thinner fake lawn stuff. There is one spot
where it needs to be flush at the steps or run it all the way down the
steps too. That might encourage rot since the treads are all enclosed on
three sides.

This only needs to last 5-10 years and we'll remodel & tear down the
deck. Plastic "linoleum" doesn't sound suitable outdoors, too slippery?