The teacher and the school may be more important that the particular martial art being taught. Consistency and interaction with others is important.
A good teacher should be able to connect with the child, and be able to handle children in a group. There is more to teaching than being a skilled practitioner. Some individuals can teach children well, some are good at teaching adult students. Some are even good at both.
Any martial art that emphasises respect for parents and authority figures will be beneficial for many children, especially if they have had a problem in this area.
Look at any safety issues with a club. There should be a clean record.
Children are more likely to have problems with accidents and falling than with direct fights, though both problems do exist. If a martial art can teach a child to handle a fall from a skateboard or bike, then you have probably prevented a broken arm, or something worse.
Goal orientation is important. Some people are encouraged by monitoring their own progress. Children often need something more that steady progress. If the martial arts programme gives out certificates or any reward for attaining a certain level of proficiency, then this can encourage many children.
If a child responds to a certain class, martial arts style or teacher then this is a good sign. Motivation can be the hardest thing to instil. That being said, don’t take the child’s enthusiasm in isolation. If there are any problems with a particular school, either sort them out or go elsewhere.