Let them sleep during the worst of it. If they want the couch to let them sleep there, the (clean) floor in the bathroom, their floor, their bed, any bed, it doesn't really matter as long as they are getting the rest their body needs during the worst parts of it. My oldest used to sleep on the kitchen floor a short distance from me while my mom or I cooked. We all knew where he was and it got to where we'd just automatically step over him. (We looked like idiots after he moved, but hey it's a small price to pay.) Let them nap in front of an open door or window for fresh air if they want. You know them and their habits, what is a comfort to one isn't always to another so don't worry to much if their favorite napping spot seems odd.
Using Netflix or YouTube is a great way to continue learning without overloading them once they are on the mend. Netflix for the documentaries is especially nice, but if they aren't feeling up to a full-length movie I'll pop over to YouTube for sound bites. YouTube is amazing. You can find any topic you want from how to math equations to read aloud books and stories. There are quite a few channels that have hours long videos of nature sounds, classical music, and other soothing sounds. It really helps keep the atmosphere relaxing if they aren't up for learning just yet.
3. Online Radio
Much like the YouTube music channels, it's great for those rough days where all they want to do is sleep. I just type in whatever music they studying and they can listen while they drift in and out of sleep. Our favorite is Pandora.
4. Read To Them
Reading aloud is also a great way to keep the gears running when they are feeling puny. It is also one of their favorite comforts. Just read a few extra chapters from whatever chapter book, the Bible, maybe a little bit from some of their readers, or even a few poems. Sometimes I'll read articles from their favorite magazines also. Sometimes they just need the sound of our voice to know we are there.
5. Books/Reading Material
I keep their favorite reading materials close to them so that they can pick up and read when they want to on their own without stressing. This counts in their reading logs.
6. Education Aids
Flashcards and lesson books are kept nearby once they are able to start working for short spells or if they want to in between naps. My daughter loves her dinosaur flashcards and will look at them for hours if given half the chance. When she's sick I give her free reign with them. Lessons are added gradually and in short bursts depending on how they are feeling.
Playing educational games on the internet or tablet is a great way to get in short lessons. The kids use them for review and quick skill boosting moments. I will let them play Minecraft a lot more when they don't feel well. Sometimes I have them build a historical home or monument, sometimes I get them to do simple math. Other times I'll let them have fun and build an original piece in creative mode or play in survival mode for a short time for problem-solving.
8. Heath Lesson
Learning about their illness on the internet or in books is one of the things the kids really seem to enjoy. Let them look up their health problems and find the root causes, treatments, and so on once they start. Encourage curiosity, just keep watch so the common cold doesn't become stage IV cancer and an inoperable brain tumor. (We've all done it.)
9. Team Effort
My favorite homeschool activity isn't really an activity at all, it's more a life lesson. When one feels under the weather the rest band together as a team to help the downed player. They learn empathy, family traditions, and cooperation. Nothing and I do mean nothing makes me feel as good as seeing my youngest pull a blanket up over someone she loves and offer her favorite dolls, or my oldest stopping by (he lives with my mom) to check in on everyone and bring soup or breadsticks from work and/or a cup of hot coffee for mom. It's even better when he runs out to pick up cold medicine or other supplies we might need. (Gatorade runs are amazing!) My second son making the hot herbal teas or a quick bowl of canned soup we use in a pinch makes my day and that of his sick sibling. When my youngest son looks up remedies or ways to help comfort, even if it's just trying not to laugh videos to lighten the mood it helps us all. My oldest daughter (my first heart baby) asking me to teach her how to make my homemade chicken soup so she can pitch in for us the way we have for her never fails to make everyone feel better. When Gran stops by with brat diet goodies and they listen to her in RN mode it helps knowing she is making sure they are doing what they need to, I'm doing what I need to, and her wisdom brings comfort and security. We all have learned the "if Gran isn't worried, we're good" lessons in life. They see teamwork, cooperation, and most of all they see and feel the love they need in order to get well in a safe and supporting environment. That is the best medicine of all.