Have you tried taking her to pick out her own sippy cup? Perhaps letting her choose will make the difference. Another suggestion....how about the 'magic' cup...one 'found' or 'captured' at the beach...or left behind by a fairy....use your imagintaion, tie it into what your daughter is fond of. If she "discovers" a magical cup she will be more prone to using it,in fact, she will probably never use anything else!!
Sometimes as parents we have to be really creative, just try and remember what it was like when we were children and had nothing but an imagination, lol. then we can find all sorts of things to use for our parenting techniques. Blend a child's creativity with our adult mentality......
Another idea, seeing the comments about giving it to the easter bunny..perhaps the easter bunny could in return leave her a new sippy cup with a note thanking her for the bottle?