The correct pronunciation is [mely'zin], which in the respelling pronunciation used in this site would be may-luy-ZEEN.
Since the standard English language has not the sound [e] excepted in the diphthong [eI], represented by the group AY in the key guide, and since most of the English speakers hear [eI] as [e] (that is why they rhyme "no way, José"), that is why the more approximate respelling would be with "may" and not with "me" (which according to the key represents [ɛ], open-mid, and not [e], closed-mid).
JHK's option (me-luy-ZIN) was not correct in relation with the first [e] and the [i], but absolutely accurated for the stress and the sound [y]. On the other hand, Shaymin's option (may-lew-zeen) was correct with the [e] and the [i] but wrong for the sound [y] and the stress.
(And since in French mélusine is also a noun, and not only a name, it has been very easy to check the IPA transcription in a good dictionary with phonetic transcriptions.)
The only reliable way to transcript sounds is with IPA transcription. Any other system will be failed because it will be always based in a language to represent sounds of another language, which means two big problems: a) some sounds will not have representation (as [e] or [y] in English); b) other sounds, different but close, will be mixed up (as the English S and the Spanish S).
That said, I agree with JHK that this site's key is not perfect (several sounds of my native languages are not in it), neither non-IPA key is, but it is a coherent and reasonably comprehensive key (it includes a representation for [y], for instance). And, most important, since it is THE key of THIS site, the non-IPA transcriptions should adhere to it. If someone thinks that it can be improved, then send a message to MikeC with the proposal, in a constructive way.