maybe you need to get to know him better..... i mean were you two really friends before you started dating?
also, do you feel simply at a loss for words, or do you actually feel uncomfortable talking to him? if you still feel uneasy around him after dating him for two months, there may be a problem.... and that is not to say that there is anything wrong with YOU, it is simply to say that maybe HE's not the right guy for you, or that you're not really ready to be in a mutually satisfying relationship. usually when you find someone who's a good match, then even if you're a quiet person, you never feel awkward in your silence, and don't feel as if you're constantly searching for things to say.
but if he's happy with the way things are, and more importantly, YOU're happy, then it isn't really anything to worry about. some people tend to be more quiet and some people tend to do more talking. however, since you seem very worried about it, it seems as if maybe you feel that you aren't actually contributing anything to the relationship, which makes it sound as if maybe he perfers being with somebody who lets him be the star of the show, so to speak, and who doesn't actually challenge him in any way. does that at all ring a bell?
so it could be a real problem and it also could not be. since you're worrying about it, though, i suspect that it is a problem, in which case you need to evaluate not your behavior in the relationship, but what the relationship contributes to your life other than just that - being in a relationship.