We also live in a small town, and my daughter began giving violin lessons about six months ago. She has had business cards printed up, but her best source of students has been her other students!
Word of mouth is the BEST advertising. In addition, her own violin instructor has all the students she wants right now, so she is referring her new callers to my daughter. So nice to have that endorsement.
Get to know some of the professional people in town. Rachael might also leave her card in public places, and mention to her physician and dentist (and anyone else she sees regularly) that she is teaching.
Gospel song "Jesus Loves Me" is well-known to many children. Here are easy arrangements to learn the music & each word to Jesus Loves Me, for early piano.