Neapolitan is a language spoken in South Italy, it's also called South Italian Language, and it can be considered a dishomogeneous cluster of several dialects without a standard.
The area where the language with its dialects are spoken has not a proper name, for this reason it has been called by the name of the most recent state existed in the area, the Kingdom of Naples (1282-1816), that covered approximately the same area of the language (with some important exceptions).
So, Neapolitan Language is NOT the language of the city of Naples, but it's the language of South Italy (for this reason is also called South Italian Language). For this reason, Naples dialect is only one of the several dialects of this language.
Here in Wiktionary there are some lemmas of the Neapolitan Language, but they're wrong, infact they are only about the dialect of Naples.
The dialect of Naples is NOT the standardized dialect of this language, is simply one of the several dialects, with its own features and characteristics.
To do list:
Since there is not a standard, there can't be a truly valid phonemic transcription valid for all regional varieties.
But a comparative approach is still possible.
Let's take the word "fuoco", a lemma taken from Classical Neapolitan. "fuoco" in this case has a metaphonetic diphtong . Regarding the final vowel, it's a //. Old Neapolitan (of Naples) had /, now it's / but it's still retained in some contexts. But in many other regional varieties / it's still used, as in Inner Campania, Avellino, Cilento, Northern Calabria.
Also the diphtong can be realized in a plethora of different ways. In Campania it's mostly , in Bari/Taranto , in Tavoliere and Ionic Northern Calabria ><.
So, if written <-o> in the ending of the word can be realized as /// depending on the context of the sentence, the regional varieties or the historical period, I think we could use /o/ as a good phonemic trascription for it.
Same for the diphtong <uo>, it's /wo/ and then could be a plethora of phonetic regional realiztion.
This approach can be useful for all those words that, even as classical Neapolitan lemmas, are broadly valid for a large amount of other regional varieties.
But still, there are two problems:
Taking again "fuoco"
the situation is something like that (with examples of phonetic variations for each phonemic reconstructed lemma)