The daunting task of wooing my buddy's out of state cousin

That title makes me sound like a horrible human being, I realize this. Here's the story:

My friend James (names and location info changed for privacy purposes) and I have been very close for three or four years. We're practically family to one another. As close friends often do, we tend to joke around with each other a lot, so when I found out during my senior year of high school that he had an incredibly attractive cousin who lived in Georgia, I immediately used it as ammunition. I would always tell him "Dude, I'm totally going to go to Georgia and bone your cousin," or things to that effect multiple times daily, usually in retaliation to similar comments out my family.

Anyway, so the year goes on. She comes to florida over Christmas break and I hang out with she and James on the evening of Christmas. She's really awesome! She's funny, very smart (now an engineering student, like myself), and incredibly down to earth, not to mention more gorgeous than I had previously thought.

More time passes, and prom season comes along. I once again start joking with James about how I'm going to take his cousin to prom and do unspeakable things to her. When he is unable to find a date, however, he comes to me and actually suggests that I take his cousin so that he can take her best friend. The two girls agree and drive down to our town for our prom, and we all have a really good time.

Fast forward to today. I haven't seen Maria (the cousin) since prom, and have only talked to her a couple of times. James and I were looking for somewhere to spend New Years Eve, and she and her family invited us up to stay at their house for the weekend. James knows of and is surprisingly encouraging of my infatuation (for lack of a better term) for his cousin, which no longer consists of the horribly disrespectful jokes it once did. He pretty much tells me "you're a hell of a lot better than most guys who would hit on her, see what happens."

So now I need to figure out how best to take advantage of new years weekend. Advice?

TL;DR I have one weekend to impress/woo/whatever my best friend's amazing cousin who lives out of state and whom I have only met a few times. Which sounds horribly creepy. And probably is.