The safest way to protect young plants is to exclude bugs from ever reaching them in the first place. This can be accomplished by using a light weight row fabric like Agribon 19. You could also consider spreading Diatomaceous Earth (DE) around the seedlings. It is totally non-toxic, however you should be careful not to breathe it. DE is comprised of the fossilized skeletons of diatoms, which desiccates insects when they crawl over it. Another very safe method is to spray a repellent like Garlic Barrier, again, this would prevent insects from reaching your plants at the start.
Beyond these general controls, if you are considering using an organic insecticide, I would emphasize the wisdom of identifying your pest before choosing a more potent control. Often times insects come out at night, so you could go out past dark with a flashlight and catch ‘em in the act in order to figure out what they are. Take a sample to a local nursery or check out a good website with pictures. I often use www.ipm.ucdavis.edu. Hope that helps!