I can use child to replace son or daughter, sibling for sister or brother, and parent for mother or father.
What is the unisex replacement for fiancée and fiancé?
I don’t need it for speech, but for formal or semi-formal writing.
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For formal writing, betrothed would be my number one choice. But, as Lunatik already gave that answer, I'll provide some more: spouse-to-be (instead of the gender-specific wife-to-be and husband-to-be), future spouse, prospective spouse, intended (date and informal).
Of course, it's much easier to refer to use adjectives and refer to the couple as a whole, if you can rewrite it in this way. This opens the door to: engaged, affianced, pledged in marriage, etc.