If the council adopts an ordinance, which is then overturned in a referendum, is the council barred for two years from trying again?

No. First, the two-year bar only applies to charter amendments that go into effect. Furthermore, as noted in Question 64, G.S. 160A-104 contains an explicit limitation on citizens being able to try again with an initiative petition that is defeated in the referendum, while there is no comparable limitation on council initiatives under G.S. 160A-102.