I find drinking coffee relaxes me. Given that caffeine is a stimulant, I would expect it to do the opposite. Why? is it psychological? does it have something to do with it being a hot beverage? is it an effect of the caffeine?
A 2008 U. Colorado (Boulder) study*, suggests that merely holding warm drinks (vs. cold) can positively influence perception of people.
There is apparently some connection between the physical act of holding a warm drink and one's perception of the outside world. The association of warm beverages and positive feelings may underlie the sensation of relaxation as well, although I didn't find a study on precisely on point.
Whether the effect is physiological or psychological the authors weren't sure.
*Experiencing Physical Warmth Promotes Interpersonal Warmth, Science, 322: 606-607 (2008) Williams and Bargh.
Coffee has many compounds beyond caffeine. There are trigonelline, proteins, carbohidrates, quinic acid, caffeic acid etc... So the chemical mix in your cup is a little more complex than just a caffeine shot. All of these chemicals are going to stimulate your sense of taste, and this effect may be relaxing, even if they are latter followed by a caffeine high.
On the other hand you have some effects in your physiology that come from drinking a hot beverage, even if it is only hot water, the temperature change would produce an effect in your body that can be perceived.
Your psychology may also be playing a role here, if you associate drinking your cup of coffee with a relaxing situation it may help you relax at a psyc level.