Clyde Thogmartin is right in his answer that traditionally Judeo-Spanish is written in Hebrew (with the quite icky trigraph <ניי> for [ɲ]). But more to the point, even when it is written in Latin script, people writing it usually make a point of not using Spanish orthography: they are putting distance between their language and Christian Spanish. Thus, per Judaeo-Spanish, writers in Turkey usually spell it like Turkish, while the Israeli Autoridad Nasionala del Ladino spells it phonetically, using <ny> instead of <ñ>. (I would assume Turkish spelling would end up doing the same.)
Something similar occurred with 20th Latin transliteration of Yiddish: it has made a point of not resembling German orthography. (19th century Yiddish text even in Hebrew script, OTOH, was daytshmerish “Germanising”, particularly in retaining double consonants, and bits of that remain in use to this day.)
Exceptionally, Judeo-Spanish texts published in Spain do use Spanish orthography, but that is because they are primarily intended for modern Spanish speakers. There has been a proposal to use 1492 spelling of Spanish for Judeo-Spanish, which would retain <ñ>; but that appears to be marginal.