My kids have participated in the summer reading program and enjoyed the filling out the chart part as well as the rewards (mostly reduced price coupons for local restaurants or activities), and I think those programs can help build the reading skills that come with practice as well as encouraging kids to look around the library for books. However, those programs weren't what turned our son into an enthusiastic reader, it was finding a series of books which grabbed his interest. He was a really late bloomer that way--it wasn't until the summer of second grade when I happened to bring home a book in the Secrets of Droon series, and it hit him at the right time. Suddenly this kid who wouldn't read more than a sentence or two out loud to me and only wanted me to read to him was reading a whole book by himself in four hours. So I probably agree with the others that if you want your child to love reading, you'll need to help her find books about topics or a character which grab her. It's possible that reading just hasn't 'clicked' for her yet. Someone suggested that the library staff could be a great resource--they can direct her towards good books about whatever interests her, and then once she is in the stacks, she may find all sorts of other books. I don't think a reward system seems necessary. If you have established limits on how much screen time she gets in a day (or a week) and she won't be outside or at camp or at play dates all day, there inevitably will be some times when she won't have anything to do except pick up a book.
I think series are a good hook for kids--the predictability of a certain scenario, certain characters, certain ways the story will end. You also might look into the graphic novel section of the library, if they have them. They're like cartoon magazines, except in book form; they range from superheros and Star Wars to Nancy Drew. While they have much less text than regular books and probably don't build reading skills in the same way, they do build the habit of turning to books for entertainment and other views of the world. I wasn't happy that our son only wanted to get graphic novels out of the library in 1st and 2nd grade, however I figured that at least he was holding a book instead of a Gameboy, and looking back on it, I think the graphic novels helped reinforce the habit of reading books for pleasure. Anyway, enjoy the summer with her!