I think institutional daycares wouldn't have tvs, but a lot of daycares run from people's homes would have them. Probably most would.
It is a long day and if it is a small group with only one care provider, that is 10 hours (or more) without a break. It is hard to argue with providers who say they need to use tv so they can have a break. It is a burnout job.
I am a home childcare provider and I used to use tv as a quiet time strategy, but have been tv-free at dayhome time for about 2 years now.
My strategy has been books on cd, as the previous poster suggested. I have all the non-napping children settle on nap mats in the same room and put a story cd on that would take about an hour to run (or I'd set it on a loop). The children have access to some non-messy art supplies, like crayons, pencils, stencils, paper and clipboards, or other special toys reserved for quiet time -- often toys that are ok for preschoolers, but not safe for the toddlers who might put them in their mouths, such as teddy bear family math manipulatives. I have a couple of boxes of these big-kid toys that I rotate, and children are allowed to pick what they want for the day. The children know they will have to help clean up any messes they make, so they are pretty good about not letting these supplies get out of control.
I tell them they needed to have time for their bodies to rest and to have a rest from playing with the other children. They know they are not to bother other children or get off of their spot except to go to the bathroom until the story was over. It took a few days, but they learned the routine and now it is as effective as TV ever was. It helped to tell them outright why we weren't using tv any more -- that it was bad for their brains, etc.
I have also had children who needed more alone time to settle rest in a separate area and use personal cd players with headphones and books to turn the pages and "read" along with the stories.
I have a couple of Disney storybooks on cd. I have been getting rid of most Disney and character stuff, but it does help to have these options available for media-addicted children who have a hard time stopping TV at quiet time. Then after a few days we transition to fairy tales on cd or something sort of familiar, but not from a cartoon, then to something really more challenging
It has been fun to see how sophisticated their tastes get. One 3-year-old girl in particular loved Beethoven Lives Upstairs and surprised her parents asking for the cd about Mr Beethoven!