Really sorry to say, no cories or neons. The Corys need 10 gallons each because they are actually really active. But you COULD get 4 Dwarf Corys. Just not the big normal ones.
Neons need a school of 6 minimum, and need 15 gallons. They are VERY, VERY active and need excellent water quality, which is harder to get in a 10 gallon.
You could get some ghost shrimp, 2 african dwarf frogs, and 4 dwarf cory catfish.
*2 Bettas (for now RIP Ryu) *2 Goldfish *9 Guppies *1 Gourami *2 Chinchillas *2 Budgies *2 Dwarf Frogs *1 Dog *1 Cat *2 Hermit Crabs *2 3gs *1 10g *1 Pond *2 2gs