Over the years we have had some late fees - Usually it is because I thought I had paid it or completely spaced it out. I simply called - and usually start with something like "Pleading for your mercy here!" and explain just what happened.
If it really was an oversight and they can see your good account history - I have had them clear it off immediately. I then thank them profusely. Sometimes they will want an payment over the phone and that is fine. They want your business.
Being nice I believe will get you much further when you are at their mercy.