Peat does wonders for that. Some books seem to imply that a coarse nylon floss is a good substitute. I would not bother, since Java moss is good enough and easier to grow than nylon. Temperatures of 70-75F are sufficient. They are said to spawn best when the sunlight hits the tank in the morning.
Neons are voracious egg eaters.
Remove the adults within hours after spawning. The powerfilters will likely suck all the newborn fry out and mince it into the fish paste, so use box or sponge filters. Infusoria and rotifers on the Java moss will feed them for a day, but after that you will have to add infusoria for a few days until the fry get big enough to eat baby brine shrimp. You can find more info in the various fish breeding books, available in the pet shops and libraries. This use to happen to me until I slowly acclimated them to new water.