I think nearly all of the stations with the Class D nighttime authorization are licensed, whether or not they use the authorization. Look it up on CDBS to see if it is already licensed. At that time, back in the late 1980s as I recall, there were a few more authorized that never licensed.
As I recall, they just had to show how they were going to accomplish the power reduction. With really low powers, they often required a low power transmitter.
You could file an application for a new authorization, nondirectional or directional, same or different pattern than daytime, as long as they are under the 25% RSS limits of all cochannel and adjacent channels. As I recall, the original authorization did not take adjacent channels into account. In a few cases, it is an issue.
In some cases, where you have a station with a really low NIF countour to be protected, even a Class B on a regional channel, the Class D can only be authorized for a few watts. If your day directional antenna manages to protect those other well protected stations at night, you could get 100-249 watts (effective). A very few can mangage Class B operation, perhaps with the same towers but a different pattern, but not likely.
If you can get 100+ watts and an antenna close to the center of the population to be served, and you are not being blasted on a cochannel where the NIF is very high, you might get decent service.
In some extreme cases, I have seen applications that had 6 towers to allow just 50 watts. The protected stations had NIFs in the 5 mV/m range, and were 100-250 miles away.