I know a girl named Rani, although I don't think her family is Israeli... I think her grandfather came from Zanzibar and her other side of the family is from India. Anyways, it's a pretty name! I like Shiri, but it has the tendency to look like it would be pronounced sheh-REE, like the name Sheree.
That makes since as I believe Rani is also an Indian name. I think it means 'queen' in Hindi. Interesting take on Shiri. I can see where the pronunciation would cause problems. For the longest time, my favourite Hebrew combo was AninaShiri. I love that name. :)