Black-skirts can be a bit nippy, and grow quite large, for little tetras! They're probably not the best bet.
Neons might do well, but they are a cooler-water fish than the Betta, so you'd have to find a happy medium there with temperature. There are also Black Neon Tetras, which are another option.
You could easily do a school of six or seven. For the Corydoras, there are some species of cory which grow smaller than others. I think they're collectively called Pygmy Cories, but I'm not totally sure because I've never looked into that. Five of these small Cories would work, as well. I would do one or the other, since these are schooling fish, and so doing half of each wouldn't really meet their requirements.
A lot of people refer to Corys as "bottom feeders" or "bottom dwellers," but I keep several of the larger types and find that they're all over the aquarium! So, don't let that dissuade you from stocking with a school of Corys. They're active, fun little fish.
Another fish to look into that stays small and looks striking in a school is the Harlequin Rasbora. You might like those, too.
I hope this helps. I keep my Betta in a 5 gallon, so he's solo, unfortunately, but I think that any of these would be fun and interesting tanks.
