People want to know that they are being heard. So really listen when this person talks. The next time they come in be the bigger person and say something like. Mr/mrs.so and so, I feel a little tension between us, is there something I could do differently for you, I would like to make you feel a little more comfortable. This should work because they get to tell you what is the matter and state their position and their solution. Im not saying you have to kiss their butts, but I think something else may be botherine them and maybe they are taking it out on you.
I've worked in doctor's offices and when people come in they are not well, sometimes frightened and because of this you may get an angry patient because they are fearful or are going through a lot of medical red tape and you have to learn it's not all about your personality or that their anger is directed at you on purpose and you need to learn to roll with the punches.. I always had a nice smile on my face, remembered their name and asked how they were. This would open up the conversation as to why they were there. I was genuinely caring towards them because I've been in their shoes. When they saw the doctor (especially the elderly) I would stop them before they left and asked how things went and then if they told me what the doctor said or showed me a prescription and that prescription was complicated (taking two different mgs. of one medicine during the day or several medications a day) I would ask them nicely to wait and I'd quickly jot down a quick and easy way for them to take this medication and certain patients began to trust me. I was just trying to make life easier for them.
Give it time and get to know the regulars that come in. I find cold and efficient medical assistants get what they deserve. You can still be efficient, but understand some of these patients can be extremely ill, angry at what problems they may have or frustrated over the red tape of the medical system and so no matter what that smile you give them or a little joking (when appropriate) goes a long way to getting into the head of a partient that is on the quiet side.