Let's see:

Aurora was already betrothed to Phillip, so she can be eliminated. Mulan wasn't lucky, she caused her own romance to happen by joining the army. Plus romance wasn't too important in her story.
Pocahontas clearly wasn't lucky. Snow White wasn't particularly lucky or unlucky. Luck wasn't factored into her romance.

Jasmine was pretty lucky, if she hadn't crossed paths with Aladdin she would have been stuck chosing someone random. Although maybe she would've crossed paths with him eventually.

Ariel was pretty damn lucky when it came to romance, for a variety of reasons. The ocean is pretty vast but her true love happens to cross right above her? And then the fact that he took a liking to her even though she wasn't the "girl with the voice". I'd say she's one of the luckier ones.

Belle was lucky too, although she got led to Beast by a series of unfortunate events rather than anything really romantic.

Tiana's was also a pretty damn lucky coincidence. Naveen confuses her for a princess. If he hadn't been transformed he'd probably end up with Charlotte. Although Charlotte & Tiana were biffles so they would've crossed paths at some point.

I say Cinderella. It was her one night to make an impression, and boy did she ever!

Belle was so lucky... find her love in a beast that become in a prince. Beautiful history!

Now see I considered Aurora to be lucky because she WAS betrothed to Phillip and not some doofus. That they met by chance, liked each other, got woken up ...it seems like awfully lucky circumstances to me but then again most of the princess are in many ways.

Wow, I agree with EVERYTHING princesslullaby said.

also Jasmine, buT Ariel was practically a different species from Eric.

Prince Charming fell in love with her immediately, and rescued her from her life of servitude. Pretty darn lucky!

Prince Charming didn't even have to meet her and their true love broke her curse!!!She's a lucky lady...er, princess.

Either Cinderella or Ariel, but I have to go with Ariel because by the time when she took risk to become a human and came into Eric's life the second time in a form of a charming mute girl she was already in love with him but he was still obsessed with the idea of the one and with the desperate desire to find her at any cost, believing this idealized image of a girl with the gorgeous voice was his true love and destiny. And despite the "mute" Ariel lacking the core identity of the one, Eric still ended up falling in love with her "from zero".

and Ariel