Catholics in Japan lived without priests for generations with only two sacraments when all priests were expelled from the country many, many years ago: Baptism and Matrimony. When priests were finally allowed to return they were amazed to find a large, thriving Catholic presence.
What did they do? I've never read any specifics. But I would guess that they married in a civil ceremony to satisfy State requirements then privately, in front of witnesses, exchanged the marriage vows of the Catholic Church.
I will pray that God sends you priests.