We have used Holmes brand cool mist humidifiers with success. They seem to be sturdy and are easy to use. Bed, Bath and Beyond stores carry them and others do as well, or you can get them online. The price range has been around $40-50, I think. Be aware that the filters are not always easily availble -- drugstores etc. don't seem to carry them so you might want to purchase extras when you buy the humidifier.
Someone said to let your child sit in a steamy bathroom -- that helps while the child's actually in there, and for a short time afterward, but I've found that (1) the effect wears off pretty quickly once the child is back in bed or out of the bathroom and (2) if you do it frequently it frankly is not good for your bathroom -- too much moisture affects the paint etc. eventually! A good quality cool mist humidifier is worth the investment and won't make the bedroom seem "steamy" or damp if it's a good machine.