Vit C probably won't help much.
You taking a multi? Thats the first step to make sure all your various normal vitamin levels are normal and not deficient.
I suggest vitamin D, and lots of it. Works for me, kills a cold really fast. I've been taking 5000IU/day for the past 3-4 months and haven't gotten sick at all. If I'm feeling a bit under the weather, I go 5000IU in the morning and at night (so 10,000IU total per day). Vit D is pretty clearly shown to be an immune modulator. Its effects on preventing cancer is dramatic. It is involved in gene transcription for, I believe, over 1000 different genes.
I just got a blood draw Friday, my vitD level is actually still low (34) after 3-4 months of consistent 5000IU/day dosing, so 5000IU definitely wasn't creating any issues with toxicity or overdose. I might even bump it up to 10,000IU per day for the month of April before the sun starts giving me my much needed UVB. BTW, I'm in Boston so during the winter months we don't get any UVB necessary for conversion to vitamin D.