If you want to focus on tutoring children who are home-schooled you will need to concentrate you marketing on parents of home-schooled children.

Be very specific on how you can help them.

There are an increasing number of support groups for parents who have decided to home school their child. If these are online forums drop in and offer friendly advice. Don’t do a hard sell, let people get to know you and trust you. Then when they are ready they will approach you.

If the groups you find are in the physical world, you might be able to pop in (via arrangement) and run a workshop with the children so that the parents can get to meet you and see your teaching styles. Again ask if you can keep in touch but DO NOT spam them as you will lose any good will and potentially a good source of tutees.