It took my dd a good solid month before she would take more than half a sip of milk from a sippy. I tried to offer it in a different sippy than what she uses for juice/water, but we ended up back with the same one. After she turned 1, she started taking about 3 oz of milk (actually, I was still using formula too until yesterday) with her meals, and I dropped the morning bottle right around 12 months. Now she gets a bedtime bottle, milk in a sippy with all meals, and water/juice during play and with snacks. Some days she doesn't drink as much, but she also gets yogurt and cheese.
How old is your lo?