I have limited experience, so grain of salt - but a 9 gallon should be suitable for a small group of Sparkling Gourami (4 or 5 max) OR up to 3 Honey Gourami (1 male, 2 females max).
Neon Tetras are pretty active - most recommend 15-20 gallon tanks for them at minimum, because they need extra room to swim.
If you're drawn to Neons for their size and color, I'd recommend looking into microrasbora like Chili Rasbora, Sundadanio Axelrodi, or Kubotai Rasbora as alternatives. They're all vividly colored and can be kept in groups of 6+ in tanks your size with non-aggressive tankmates. My 10 gallon currently has a single female Honey Gourami, a shoal of Chili Rasbora, and a colony of dwarf shrimp, and they all coexist pretty peacefully.