You'd think a sick child would welcome the opportunity to stay in bed and rest. You'd be wrong, of course. Never mind that staying in bed is a good way to get mommy to take care of you or to get out of doing chores -- although you might want to mention those two things to encourage him to stay put.
Pick your battles when it comes to staying in the bedroom at all times. You might have an easier time dealing with a sick child if he can spend some time sprawled out on the sofa or a comfy armchair near you. Sick children want attention and to be babied, and that can't happen if they're in a different room.
Move the TV to the child's bedroom if he doesn't have one. This is the one time when the TV can become your best friend. Even better, don't let your child watch TV in any other room except his bedroom, so he has no choice but to head back there if he wants to catch his favorite cartoon or movie.
Sleep in the bedroom with the child if he's feeling very sick. Sleeping on an armchair or an air mattress next to the bed is probably not your idea of fun, but it will make soothing your child through the night a lot easier. Just keep in mind that sick children often have trouble sleeping and will toss and turn and then toss some more. Don't expect to get your beauty sleep for a few days.
Give your child a bell or another item he can use to call you when he needs you. If he knows you can hear him, he might be more willing to stay in bed. Keep in mind this probably means you'll be his slave and will be called a million times, just for the fun of it. In fact, you might have to reconsider this for very young children, who might find it funny to ring the bell 10 times in five minutes. For older kids, it could be fun to have you "serve" them for a day while they rest in bed.
Come into the bedroom regularly to spend time with your child. Bring a kiss or some crayons to break the monotony of staying in bed. Or bring your laptop and do your own thing. Some children just want the company, even if you're busy doing something else.