The current gen Honda City diesel will not get a CVT gearbox according to Honda. The car maker had raised hopes of a diesel CVT in the City after the all new Amaze was revealed at the Auto Expo with a diesel engine CVT box combination.
The current City is already half way through its production life cycle so time and investment for for a diesel CVT model is not justified. The next gen City will be out in 2020 and that model could get a diesel CVT variant. Honda officials have also said that they are evaluating more models for the CVT gearbox and the City is definitely one of them.
Honda has already started testing BS VI emission norms compliant version of the 1.5 litre i-Dtec engine. The company has said that diesels will continue to be an important part of their model line up.