A Dwarf Gourami fish with 4 Neon Tetra fish in a 1.77 Gallon Tank?

No, it's FAR to small. Maybe just the neon tetras for the time being and maybe you could get a bigger tank? I have 6 neon tetras, 4 ghost gl catfish and a Khuli loach (not sure if thats spelt write :]) so maybe you should think about getting a bigger tank or less fish.