Why not just have your sister get her an iTouch? It does everything your phone does except for calls--except that she could Facetime with you or anyone else in your family with an iPhone, iTouch, iPad, or Mac computer (then she could even show the family member her "injury"
. With the iTouch, she'd have all the apps, games, camera, and everything she's used to on your phone. My 3yo loves my iPhone. She loves to Facetime with her Daddy if he's working late or with her aunts/uncles/grandparents (we have a lot of iPhones between my husband's and my family). IMPO, an iTouch would be a good compromise without having the added expense of minutes each month.
Then, you could take the savings from not having minutes to pay for each month and use it toward some gymnastics lessons or special activities (monthly Mommy/Daughter date)? My 3yo has been in gymnastics for a year now. She loves it.