I give my lo the amount of milk she needs, but I water it down with water. Maybe sounds cruel, but she doesn't drink enough water and has a constipation problem when I don't.
Another idea is to have your lo drink small glasses of liquid out of tiny plastic or paper disposable cups. In the US we may call them bathroom drinking cups.
My lo likes to drink out of shot glasses or small glass votive candle holders (they look like shot glasses). They are perfect for their little hands. We learned that trick from the Montessori schools.
Some lo like to drink from straws.
Someone else mentioned the sports drinking spouts. If you lo has trouble with them, they make ones for kids that can be put on all (adult) plastic water bottles.
Somedays my lo likes cold drinks with ice cubes and other times she wants her liquids warmed up. Maybe try both. I was ready to give up on a particular sippy cup just this week. Then, I decided to give in and warm up her milk again.
Praise sometimes works. We say, "cheers" and then click our glasses together.