I had the same problem with my son. In order to get him to drink from the sippy cups in the first place I had put water-filled cups all over the house so that they were there whenever he wanted them. I also went through a ton of different cups before I finally found some he'd drink from.
When it came time to pull the bedtime bottle, he totally refused to have milk in any kind of cups. Eventually I had to take all the water cups away and only give him one AFTER he'd drank a certain amount of milk at mealtimes. Every meal I'd give him a half sippy cup of milk and tell him he could have water after he'd finished it. I'd make that cup follow him around after the meal until he drank it or it started to be long enough that I'd replace it with fresh milk. We wasted quite a bit of milk during that period. Otherwise I gave him some water now and again (he had a water sippy cup we always took in the car and usually got water before bed - boy did he suck down water when he got his hands on those!) so I knew he wouldn't get dehydrated. I was also trying to sneak cheese and yogurt in on him to make sure he got the calcium in the meantime. On top of that, my husband and I would make a point of drinking full glasses of milk with our own dinner, right in front of him, to set the example (I HATE milk myself - I normally take calcium supplements instead!). Then we would tell him that once we'd finished OUR milk, we could have something different to drink afterwards too, just like he did. He finally adjusted and has milk with breakfast and lunch consistently and sometimes even asks for more after dinner.
The only thing is I STILL (he's 3 1/2 now) can't get him to drink anything OTHER than milk or water. He'll try juices occasionally, but generally just a few sips and then he'll ignore it. That's not as much of a problem, however, since most of those juices are sugary anyway. I make sure he gets fruit with lunch most days, so he's getting the nutrients that juice has in it.