Be sure to use an example of a time when you managed a conflict in a positive way. Keep your answer work related and be sure to talk about any kudos you were given for your ability to mange the conflict in a positive way.
"I am generally very good at managing conflict. One example that I can give you is quite recent. Last month I had a client who had been over-billed in error. They were quite upset with the oversight as they are a long term client. I ensured them that our billing department would review all of their previous invoices to ensure this was a one time incident. It turned out very well and they appreciated my transparency and willingness to solve the problem immediately."