Listen, listen and listen.
Understand their points or concerns, and let them know you will do everything you can to take care of their problem/concern. If it concerns a difficult customer you are trying to sell, you need to rationalize with them and reinforce the benefits that the product can do for them. Most importantly, keep your cool and composure. Always try to make a friend, even with difficult customers. Win them over and they will be yours for life, and they tell EVERYBODY!
Let them vent a bit especially if they're being difficult for just a specific instance.
If an ongoing issue, set up a personal meeting away from their office setting and try to make the personal relationship stronger. Over communicate, try to beat his/her expectations on everything, ask a ton of questions, confirm what he/she wants/needs and ask what the vendors he/she does business with do that he/she likes.