In your cover letter, you may want to mention specific examples of when and how you used your customer service skills. For example, if you worked as a hotel manager, you could write:
During my time as a hotel manager, I ensured all customers had their needs met within minutes. Particularly during the changeover period between check-in and checkout, occasional problems would arise where some rooms did not get cleaned in time. When this occurred, I always ensured that guests rooms were cleaned immediately and within minutes, and offered complimentary items to help rectify the mistake.