Sadly, colds are colds and have to run their course. I believe the best thing you can do is to keep them strong and healthy so they don't get sick in the first place. Here's what I do/did for my sons (now 14 and 18)...
1. Healthy diet rich in protein, fruits, veggies and light on junk food.
2. Stay hydrated, water and milk preferred.
3. Get lots of sleep every night.
Kids need a lot more sleep than we realize. We follow the "early to bed, early to rise" concept. My 14 year old is lights out at 8pm and my 18 year old at 10pm. Most of my students (high school) gasp in shock at this and then say, "I wish my parents would make me unplug and go to bed early." My boys sleep as much now as they did as toddlers and I make sure they have schedules that accomodate that (as best as possible, of course).
4. Daily bathing and washing hands after the rest room, before and after handling food, etc. Never underestimate the power of soap and hot water!
I know it seems too simple and too good to be true. Yes, they still get sick but the above usually keeps time out of school down to one or two days.
As for the cough, humidifiers are great but they can get moldy. I have the Vicks menthol pad warmer which puts out a great menthol/eucalyptus smell into the room which works wonders on coughs. On the really tough coughs, Vicks Vapor Rub. For the horrible, I can't sleep coughs, nothing beats Nyquil. The best way to beat a cough is tons of rest and water. I let me kids cough everything up during the day but make sure they have whatever it takes to sleep well at night. No one gets better if they're not rested. I had a vicious cough for 18 months and, really, it only went away when I got an unexpected three months off my after school job. I went home and rested every day and voila! No more cough! Memo to me...
Good luck!