Piano Methods and Children's Personalities
Piano methods and children's personalities must match almost perfectly. Otherwise the job will become stressful for both teacher and student. The younger the child, the more this is true. If your prospective piano student takes to reading sheet music like a duck to water, then you might be able to get away with the standard book based piano methods. But most kids like reading music about as much as a trip to the dentist, and that's the truth. There are ways around this attitude, but none of the solutions are quick and all involve extreme patience and effort on the teacher's part.
Make The Beginning Palatable
To impose a piano method that the child finds uncomfortable is a recipe for disaster. We're not talking about endlessly coddling kids. We're talking about finding ways to make the start of piano lessons enjoyable enough for the child to want to continue. Regardless of a child's personality, if they are having trouble reading music, you had better find other ways to keep them interested.
Making Music Like Finger Painting
The most prevalent trait of children at the piano is the impatient desire for instant mastery of a specific song. It may be a song they know, or one you show them. Simply put, children want to make music at the piano, however sloppy. When you finger paint, you expect a mess. Think initially more of play than work. Thus if you can get a child to play even a few notes of a song they like, you have a chance of launching them happily. Take Jingle Bells as an example of a song. (Obviously, if you are teaching a 10 year old, you'll have to think of more stimulating material.)
If you can get a child to play, with one finger, the opening notes, they will light up and realize they just made music. Why did they enjoy it? You didn't impose reading music, you didn't impose fingering, and you didn't impose rhythm. You simplified the material until the child grasped the essential fact: this is music and I can play it on the piano. The simple act of making music, however humble, is not lost on children.
Feed The Fire
They will want more songs, right away. Kids will respond if you are careful to simplify the material so it is within their grasp immediately. Repeat the above experience with dozens of songs, and you will have a child who trusts you. The child likes making music at the piano, and is eager to learn more. But the music must be couched in terms they can easily understand. With such a student, you can make a slow, easy transition to reading music without risk of losing their initial enthusiasm.
If They Don't Resist, Read Music
If a child demonstrates a desire to read music, apply the same rules to that discipline. Simplify as much as possible. Without initial enthusiasm, you have no fuel with which to travel through the intricacies of beginning piano. Your first job as a piano teacher is to awaken enthusiasm, not begin the indoctrination of the child with your piano method.