Try to find a good reason to make them think that astrology is wrong, better reasons, better prepositions, astronomy.
The more likely it is they will start thinking scientifically the better. Some people who believe in astrology believe that to know about planets is the ability to predict the people's personality, future, and to have no doubt of what kind of life this person will have depending in its zodiac sign. I would find good reasons to make them doubt about what astrology propose, than, I think they cannot have a good reason to believe in astrology. But how? and why take their believes away like a father taking the candy from his beloved kid?
In the first question of the how, I would try to explain the laws of physics and demonstrate that gravity is stronger on an apple being hold by your hand than the gravity of a planet affecting on you. I would try to demonstrate through out perception, introspection, memory, and reason that the constellations in the sky are no entirely still, that stars move like planets and that they have nothing to do with your personality; I would try to show them how mathematics works to explain the physics behind nature so they can have reasons to find the scientific method more interesting by learning more scientific background.
Just like they were the very same Babylonians who thought and reasoned the misconception of the position of planets having an effect on you. I would try to make them think that hepatoscopy is not the way to know the future just by explaining that the liver is an organ, that you only have one and is not meant to sacrifice it for the gods to get your future revealed by the their made up gods. Teaching them real science would make the astrology believers, them who have no reason, to not doubt what's disclosed to them through perception, introspection, memory, or reason than what they are justified in believing through astrology.