Neither. Use the word "gender" here. Or better still: Parents have no way of choosing whether their child will be a boy or a girl. The original sentence was just too clumsy.

Wow...difficult question. We all know we could say, "Parents have no way to choose their CHILD's sex." However, this is confusing because we can 'choose' one thing, or we can 'choose' many things. We could say, "I chose the dresses for my children's high school banquet." Or, "I chose my children's dresses." We can also use the single form of a word and say, "I chose my children's room in the new house." This is supposing that they share a room together. Notice, we cannot say "I chose my children's room" if the children don't share the same room. Similarly, we can't say "Parents have no way to choose their children's sex" unless we are sure that the children that we are talking about share the same sex (all are male, or all are female). Since this is a general statement about all children, we should say, "Parents have no way to choose their children's sexes." Also, this sentence is correct, but I think a more natural way of saying it would be "Parents have no way of choosing their children's sexes."

First of all, use CHILD.

Parents have no way to chose their children's sex. this one explains the meaning better because the quantity is not important in this sentences

Parents have no way to chose their children's sex. Sex can be male or female.