It may not be to her taste, but she might have some success with country music.
Why? Usually, the melodies are fairly basic. Verses and choruses follow a predictable pattern; get the melody of one verse and one chorus down and you can do all of them as necessary. The range of notes in a country song is generally small and does not require the vocal gymnastics of a Whitney Houston or a Celine Dion. The beat usually stays the same throughout the song as well.
Note that the above is a generalization; there are country songs that do not fit the above mold. But many do, and my wife, who also has a beautiful voice, but is reluctant to use it at karaoke unless she can find an “easy” song to sing, has had some karaoke success singing country songs. Her favourite karaoke songs include Kathy Mattea’s “Eighteen Wheels and a Dozen Roses” and Mary Chapin Carpenter’s “I Feel Lucky,” among others. The latter can almost be spoken in parts as long as the vocalist can follow the beat–let’s face it, there isn’t a lot of melody needed to say “Hot damn, I feel lucky tonight!”
As I said above, country may not be to your sister’s taste. But she may find more success there than with some other genres. Anyway, the point of karaoke is to have fun, and I hope that whatever she chooses to sing, she has a good time.