When did high school night school programs begin in the US?
I believe it started back in the day of slavery. I do not have an exact date however, some people that were deemed not worthy of an education (i.e. slaves) studied academics secretly in the middle of the night in secret groups. These schools were called Moonlight Schools. Although the above answer is informative, it has little to do with the "high school programs" specified in the question. Slaves were usually denied any opportunity for freedom of thought and were heavily discouraged from gaining any knowledge, even about their own culture, to the point of violence from their owners. I find it hard to imagine that slaves would risk organizing these "schools" in any large number before the Abolition of slavery. Are you trying to describe a post-Civil War black education movement?
Still it doesn't explain what the question means by high schools.