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.