If you do give them Nyquil, only give them 1/2 an adult dose. This medicine isn't meant for children. I know it helps them sleep, but the dosage is for an adult. If you have the children's Nyquil brand, that would work better for them.
An estimated 7,000 children under the age of 12 are treated in hospital emergency departments each year from ingestions of cold and cough medication, and over 100 children have died from them in the past 40 years. In 2007, the FDA recommended the removal of all infant cough and cold preparations from the shelves. Studies have shown that they aren't particularly effective in relieving symptoms, and clearly they can be dangerous.
We gave my 15 y.o. (140 lb) son Tylenol cold capsules last year and he was so out of it for more than 24 hours we ended up at the ER! Their systems aren't like adults, and handle colds meds differently.