Generally speaking it is forbidden to rely on any means of divining and controlling the future by supernatural means; Astrology would certainly qualify. While pru u'revu is a very important mitzvah, the ends do NOT justify the means. Additionally, I am very skeptical about the reliability of a method that predicts the sex of a fetus based on the birthdays of the parents.
However I did find a many websites that can calculate the days most likely to conceive a boy based on the based on a certain degree of medical theory regarding the proximity to ovulation. While their method is by no means fool-proof, it at most increases the odds of having a boy and that by a modest percent, if your brother is willing to give it a try there would be no issues in Halacha.