Not only is they the obvious alternative, it's always been perfectly good English and has been traced back to long before generic he was introduced—by Latinists

Not only is they the obvious alternative, it's always been perfectly good English and has been traced back to long before generic he was introduced—by Latinists who wanted to make English more proper in I forget which century. Now that generic he is rightly getting dumped, the natural solution that existed all along—singular they—is making a comeback. It's a lot better than stilted fabrications like "he or she", "s/he", and the hideous "ostentatious she" that some people (seemingly always liberal males) insist on using to denote programmers, venture capitalists, and other demographically lopsided populations—as if changing the ratio of pronouns would change the ratio of people. The fascinating thing is that generic he was an ideological construct in the first place, a top-down imposition that never fully caught on in English despite literally centuries of being proclaimed as proper. Singular they continued to be used the whole time, and is found in most (all?) great English writers. (Jane Austen was particularly fond of it.) I don't have citations handy, but people with similar bees in their bonnets have made sure that web searches won't lack for them.