I took piano for 12 years, from K-12th grade. I am so glad my parents didn't let me quit. Mom would set the timer and have me practice 20-30 minutes a day, depending on my age. With my own children, 10 and 7, we have a reward system. (Let's face it, practicing the same scales and songs over and over again is boring!)
1-When they first started their lessons, we did a chart. We checked off each time they practiced. After so many checks, they got a reward. I gave them the rewards, or the piano teacher rewarded them, or I helped fill the teacher's reward box.
2- We also split up their practice schedule. They would practice about 10 minutes each morning and 10-15 after school. This helps with their low attention span.
3- As my kids have gotten older, the almost 1:1 reinforcement has become monthly rewards. They get to go out for ice cream(which we do as a family anyway) or a trip to McDonalds. We make it special.
4-Another motivation for practicing is song choice. As my son entered 4th grade, he was ready to quit. At the same time we had to switch teachers. The new teacher let him pick his own song (i.e. Star Wars, Indiana Jones) and he would get a page a week, as long as he practiced daily.
5-We give our kids days off from practice too. They may only practice 5 days a week, with the weekend off.
6-I have promised my son that if he gets really good by continuing to practice, he can pick another instrument to learn.