Thank you for those useful comments.
I must say that for me the idea of a compelling conversation has to be something that the STUDENT finds compelling, and no two people are the same.
So a big tip for me is to ask the student to bring in topics that he or she finds interesting. He or she may be a passionate speaker builder, in which case you may have to learn to find that subject compelling - hardly an easy thing to do but then these lessons are not about the teacher, they are about the student.
Hope that helps!
Shelley
PS For teaching children privately see this video:
How to teach a child to speak English
And for online teaching, either in a virtual classroom, or as a private tutor, for kids and adults, see this book:
ESL Online Games