In good clean water within reasonable parameters, well fed Neons will court and scatter eggs in a community tank. They won't survive, but in essence at least, Neons are not difficult to breed.
The usual rules about seperating the breeders, and protecting the fry apply equally to all egg scatterers and Neons are no exception.
What makes Neons, and indeed, most blackwater fish a problem, is the blackwater conditions. These fish have evolved in water that is pretty much salt free, (and I don't just mean NaCl salt, I mean salts in the widest sense). The water has almost no hardness. I have collected tetras in blackwater creeks off the Rio Negro and the pH was to low for my equipment to measure, i.e. less then 4. In a large open body of water like the Rio Negro, the volume is sufficient to stabilise it, but in a tank, it is very unstable, and can swing rapidly and extremely in pH, usually with fatal consequences.
At the same time, just a few ppm of Ca++ ions in the water will prevent Neons eggs from hatching. The Calcium reacts with the egg shell making it too tough for the fry to emerge.
Once hatched, the fry are small, but no more difficult to raise then many other egg scatterers. They can be aclimated to more stable water after a few weeks.
Black Neons or Glowlights are a lot less demanding.