Pick weaknesses that are not a core skill for this position. You can be candid in your answer; recognizing that you aren't great at something and acknowledging your need to improve. Be sure to have an action plan in place for improving on this weakness.
Perhaps you are watching TED talks to gain skills in a particular area, reading the latest-and-greatest book on the subject, or maybe you are taking a seminar at a nearby community center. We are all human with our weaknesses, so don't be afraid to share yours!
"I believe I could improve on some technical skills including Excel and PowerPoint. Currently I am at a beginner to intermediate level; however, I would be more comfortable at an advanced level. I have enrolled myself in an evening/weekend workshop for the next six weeks. We will see how stellar my skills are after that course!"
"Everyone has weaknesses. I tend to be too nice sometimes. When vendors are not fulfilling their requirements, I tend to believe there must be a logical and understandable reason. I have to remind myself that we are paying for a service and they must meet our expectations."
"I know this will come off as cliche, but it's truthful. My weakness is not delegating. I know what I want and how I want it done, so it's often easier to do it myself. However, it can inhibit my ability to grow. I cannot take on every step of a project; I need to be able to give the task or a portion of it to another team member or direct report, let go of the control and know it will be taken care of. I've spoken with my current manager about it, and we've developed a system where he can call me out on the behavior since often I'm not aware of it. By bringing awareness to it at the moment, I find my propensity to hold onto control has decreased, so I'm certainly moving in the right direction."