Is "youth" gender-neutral when countable?
Solution 1:
Oxford Dictionary of English defines the countable noun youth as 'a young man'; Collins English Dictionary defines it as 'a young person, especially a young man or boy'; Merriam-Webster's Collegiate Dictionary defines it as 'a young person, especially a young male between adolescence and maturity'; American Heritage Dictionary defines it as 'a young person, especially a young male in late adolescence'.
This probably happened because the countable noun youth was used mostly to refer to males at the time the lexicographers composed the definitions. Indeed, you can use it to refer to both males and females, given that three of the four definitions cited here allow for it, using only the qualifier especially and not exclusively.
Solution 2:
In sociology/social work, youth is a gender-neutral term referring to people in their teenage years (especially the late teenage years) and their early twenties. It is especially common in the phrases at-risk youth and homeless youth.
I spent some time writing about the child welfare system in a state where people were eligible for services up to age 21. I was encouraged to use children and youth as the collective term for the people served by this system. This frequently involved gender-neutral count usage (e.g., "about 9,000 children and youth are in out-of-home care").
Here are some examples of gender-neutral count usage from around the Internet, mostly with additional modifiers "at-risk" or "homeless" because they are easier to search for:
Many examples, e.g., "a number of youth identified the theme..." (PhD dissertation)
Many examples, e.g., "Only two youth I interviewed..." (book)
"Five youth were living in foster care..." (book)
"twenty-three sponsored youth participated in a life-changing experience..." (organization website)
"One-in-three 'at-risk' youth in school..." (book)
"Three at-risk youth have been awarded scholarships" (radio transcript)
"...intervention plan for four at-risk youth." (PhD dissertation)
"Matching of [four/two/an] at-risk youth..." (organization website)
"...for eight homeless youth, ages 16-21" (organization website)
"One of the tech-savvy, ask-risk youth has a question" (newspaper's blog)
"A special programme places 2,000 at-risk youth..." (The Economist)
"Troubled youths" (The Economist)
"...all homeless youth had beds." (NY Times)
I don't know the extent of this usage - it seems clear to me that it is accepted in American social services, and is perhaps especially common in the Pacific Northwest. I do think the usage is not limited to social service clients and professionals. For example, most every episode of the Savage Lovecast, one of the top 20 podcasts on iTunes, mentions production help from a group of "tech-savvy at-risk youth". At least one member of this group is female and the term is sometimes explicitly numerated as in the last link in my list above.
Wiktionary gives a definition of youth as
(countable) A young person.
albeit without citation. The following definition is "A young man."