From what I can find, the "Au" is pronounce the same as in "Maui" - that is, like you just stubbed your toe and are saying "Ow" that hurts. Then, the rest of the name rhymes with "Johnny". So - say it "owlonny"
By the way, Aulani means "royal messenger" or "heavenly traveler".
HOWEVER, I found a few press release items where Disney or the reporter say various things! KO OLINA, HI Walt Disney Parks & Resorts has announced the name of its new resort in Ko Olina, HI: Aulani, A Disney Resort & Spa, which is scheduled to open in 2011. Aulani (pronounced aw-LAH-nee) means the place that speaks for the great ones or the place that speaks with deep messages.
Once completed, the beautiful Aulani (pronounced ow-lonee) resort will be another unique Disney experience for travel agents to sell, and one which surrounds clients in the lore of Hawaii and its rich stories, said Randy A. Garfield,