Hi, if it's help with constipation you might want to think about diluting some fresh orange with the water ration one in ten. I'm not sure whether the type of cup matters, my LO wouldn't take anything except when feeding from the breast. We tried bottles and cups etc and she would just bat them away - she would play quite happily with the mouthpiece and chew it, but as soon as she detected liquid she would screw up her face. After a while of trying different things we decided to stick with a very simple cup with a rubber spout and offered her the cup little and often. She slowly came round to the idea. Sometimes we have to hold the cup up for her, other times she's happy to hold it and drink herself. We have now stopped the juice and she still drinks plain water from the cup.
HTH
Tina and Kate