How old are they?
If they are young (elementary) then (particularly since you expect they may be home tomorrow as well) I would try to pick up their missed work from school, or at least find out what of it they might be able to do at home with what materials they have. Are they reading anything in history, or have vocabulary words in language arts? Science vocab or reading they could do, if their book is at home with them?
Since they seem to be in good spirits, I'd have them try to keep from falling behind in whatever areas this is possible to accomplish. And yes, TV would be ok.
What would not be ok, is running around outdoors, having friends over, going out to eat/mall/stores, etc.
Part of staying home is keeping others from exposure to whatever illness they have. The other is rest.
If they are older (middle/high school) then I agree with Angela... kids miss WAY too much to be able to stay home if they aren't really sick. And most kids know that it isn't worth trying it. I always hated being sick and almost never stayed home when I was in high school, unless it was a stomach bug. Cold viruses... meh... it wasn't worth missing, even if you weren't up to par.
Also, it is completely normal for kids to feel really poorly upon waking in the morning, and as the day progresses for them to feel better and have more energy midday, and then they may be a little active. But it will wear them out faster than normal, and they will decline towards dinner, often times.
Your attitude about it will matter more than whether or not you allow them any TV. I'm not a fan of "personal days". If you are sick, you are sick. If you just want to lay out... then you are lazy. That's my personal opinion. Keeping your kids from watching TV won't prevent them from thinking it is ok to stay home if they aren't really sick if your overall attitude towards it is indifference. And they will pick up on that aside from allowing TV or not.