What other species could I add so that they would still live "in peace", i.e., without eating each other? There's some free space, so the fish size won't be a problem.
Neons and black skirt tetras* are both easy-going fish, so you won't have much problem with them being aggressive to newcomers. As long as anything you add isn't highly predatory/aggressive and isn't too huge, they'll probably play nice. (Bear in mind that if one fish can fit another into its mouth, it probably will at some point.)
One thing that I'm not 100% clear on is whether these are the only fish in the tank. If so, it seems like you've got the upper/middle of the water column in your tank pretty well stocked, so I'd look at some bottom-dwelling fish. If you want to keep the South American theme -- which isn't necessary, but does make it easier to pick your target water conditions -- you could look at adding a handful of corydoras cats.
If you've already got a bit of a community setup and are looking to add more schooling fish, there are tons and tons and tons of options. Aesthetically-speaking, you've already got a nice contrast in color and body shape between the two tetras though, so you might just want to fill out the black skirt tetra school if you've only got a few.
*Just another common name for your black tetra; same fish.
If you want to add some larger fish that aren't a threat to your neons, here's some of the more interesting ones. I'm listing only hardy fish, there's number of other good ones like discus, but they have specialized requirements for care and are an expert level fish only.
Freshwater angelfish (can be risky but generally considered safe, start with small, captive bred, ones for best results)
Peaceful cichlids (Bolivian rams or apistogramma's)
Most gouramis (dwarfs and smaller ones are always safest)
A single male beta (can add several females safely)
Harlequin rasboras (Most rasboras are safe)
Molly, Platys, Swordtails
Plecos (Stay away from common and large ones, stick with bristlenose IMO)
Most other tetras (Congos are a beautiful larger tetra)
Make sure you aren't overstocking and you either quarantine or buy extremely healthy stock when you are adding to an established tank. The last thing you want to do is introduce a pathogen into a display tank.