It could well be that since none of the other cousins are invited, you aren't either. We had to do that with our wedding. We were limited on space and my mom has over 50 cousins (with spouses). I am close to a few of them since they lived near us and we spent lots of holidays together. I wanted them there. But I couldn't invite 2 out of 4 sibs and I couldn't stop at "these cousins but not the rest" so none were invited. In fact, none of our friends were invited for the same reason; by the time we were done with family, there was no room for friends. I felt terrible, but most understood.
If you are growing resentful, either pull back and realize that there are tons of reasons why you didn't receive an invite (anywhere from no cousins, nothing personal, to the invite got lost in the mail) and move on with your great relationship with them, or ask (nicely) why you were excluded and offer up the gift anyway. Think hard about outcomes here -- be prepared whatever you decide so that it doesn't blow up into something that derails your relationship.
I would call instead of email, since the tone doesn't come through in writing all that well, and you don't want to be accused of being snarky. Contact whichever one of them you are more comfortable with, and ask about the party. Tell him/her that you have a gift for the LO that you were planning to bring to the party, but since you weren't invited you'd like to bring it by whenever is a good time for them. Or say something like since you won't be at the party to help celebrate, you'd like to have a "family" party with your family to celebrate the birthday. Have them over for a barbecue or something. Then if they still don't explain, and you REALLY want a reason why, just ask and say that you're curious as to why and you hope it's not b/c of any upset on their part with you.