We don't set certain time limits and our kids don't earn TV, kind of like they don't earn food- I want them to learn healthy habits, not see it as something they constantly strive to get.
We just don't make a lot of TV watching part of our rhythm. Sometimes we'll watch an episode of something (usually food network) in the evening, but when it's time to turn it off, it goes off. We enjoy documentaries as part of school a few times a week.
My girls are 10, too. I think it's plenty old enough to understand that there are times to unwind with the TV, but it doesn't have to be constant. If you say no, it's no.
If they are asking all the time, make a rule that the TV only gets turned on on the weekends and leave it that way until they develop better habits.