try different cup, using a straw, a "normal" plastic cup,etc until you find what works! Murray only drinks water and is happy with it = my friend's LO drank water too until she was given juice and now only will drink juice (my theory is that if they don't know any better they will take what they know!). You can get a filter jug and leave it out at room temperature so you don't have the coldness factor ....
Your title says that he has diarrhoea - if so, breastmilk is probably best for him to keep him hydrated. When Murray was ill he would have more breastmilk then revert back to cows milk and water once he was better. Also if you go to the chemist they can prescribe the rehydration sachets without going to the doctor ...