"What would you change about yourself?" is essentially a modified version of the conventional interview question "What is your greatest weakness?" In essence, the strategies you should use in responding to the "change" question is similar. The ultimate goal is to come across as genuine, human and likable, but not incompatible with the job or company.
You need to understand the hiring manager's purpose in asking a question to effectively answer it. In this case, a manager wants to find out if you have grace under pressure, can perform genuine self-assessment, and are compatible with the needs of the position. Your answer ideally includes elements related to all three. By researching the job ahead of time and comparing the qualities desired to your strengths and weaknesses, you are more prepared for any version of the weakness question.
A good starting point is to select a truthful, but relatively minor quality that doesn't correlate to the job. You might say "I wish I could bottle up the energy I have during the day at night when I'm with my family. A lot of times, I'm exhausted by the end of the work day and struggle to have the same level of activity at night." This answer shows a genuine thing that you would like to change, but it evades any impression that the change would affect your work performance.
Shift to Positive
In using the "exhaustion" example, you subtly point out your strong work ethic and high energy on-the-job. You can craft a genuine thing you'd change and include a positive note, without sounding trite. For a manager position, you might say "I tend to have especially high expectations for my employees, so I have to work hard to balance motivating strong performance while still showing concern for my workers as people." This answer shows that you realize the potential for being overly critical, but you self-monitor by balancing two key elements of effective management.
Closely Related Questions
The question "What would you change about your personality?" is very similar. Your answer just needs to center on a personality trait. A distinctly different question is "If you had to live your life over again, what one thing would you change?" In this case, you want to focus on a missed opportunity or challenge where you made a wrong choice. Choose something from the past and talk about how it sparked growth and development and what you would do different today. You might say "I regret not finishing my degree sooner, but having to finish up while working and managing a family helped me learn multi-tasking, hard work and perseverance."