It was hard for me to overcome elementary-school inhibitions and go with 'they', but Shakespeare really helped. Here's the Bard using singular 'they' when the gender of the person being referred to is unknown:
FRIAR LAURENCETurns out that singular 'they' was used a lot in the old days before 18th century grammarians came along and cost us a useful pronoun. Of course, singular 'they' isn't perfect, as in some cases context will leave it ambiguous with the plural 'they.' But 'he' and 'she' have even worse ambiguities, some of the other options are hard to say, and 'zie' is just too weird.
Arise; one knocks; good Romeo, hide thyself.
Not I; unless the breath of heartsick groans,
Mist-like, infold me from the search of eyes.
Hark, how they knock! Who's there?