I would completely agree with Joe – keep getting the word out there, so many people are interested in learning to sing and even if they aren’t for themselves it is often a great idea as a present for someone else:)
In addition, I would really recommend introducing yourself in local music shops and really getting to know the staff, as well as connecting with other music teachers locally – word of mouth enquiries really still count for a lot of teachers enquiry streams.
If a teacher cannot take a student on they might be happy to point them in your direction – especially if you specialise in a specific area of piano tuition. Becoming involved in such a community also means that you can direct students who might be more suitable with another tutor over to them – keeping both students and teachers happy.
Hope this helps:) my biggest advice would be to introduce yourself to the people in your local music tuition community, great place to get the ball rolling & also met some really interesting people along the way!
What are the ways you are currently generating enquiries?:)