My neon dwarf gourami is always sitting underneath the breeding net.
I just remember reading that they like to have floating plants that they can hide under, so since he doesn't have any plants available, I guess he's taking the next best thing which right now is the net.

What kind of plants could I use? My LFS has floating ones (with very small leaves) but they start getting yellow and fall apart after a few days and make a big mess!
I don't really know if they are supposed to be used for that or if they are merely for feeding purposes.
Is there anything that stays alive and clean? I would like to stay with real plants though, no plastic plants.

I know this is not a floating plant, but java Moss would be good. You said they like to hide, well java moss is good for hiding small fish.