попробуйте подать документы на партнерский ВНЖ (без брака)

Dependent Partner of a Cypriot citizen with a duly proven permanent relationship for the purpose of marriage. The specific temporary residence permit is issued for three months and concerns foreign nationals who maintained a duly proven long-term relationship with a Cypriot citizen (at least one year) and who entered the Republic by legal entry with a visa and did not stay in the Republic for more than three months after the expiry of their visa.

подача в Никосии по живой очереди (слот не нужен). Список документов посильный (но нужна справка о несудимости из страны происхождения)