Coricidin is very, very bad for you. I don't feel comfortable offering any advice as to how to take it; my only advice is, don't. If someone asked how to make arsenic poisoning come on faster, I wouldn't want to help them with that, either.
Go to the drug store, spend 5 bucks and buy a DXM product that won't cause permanent damage or kill you. Coricidin has chlorphenamine in it, which can KILL YOU and makes DXM itself worse for your body by competing with a key enzyme that metabolizes it. It may actually be MORE irresponsible than huffing paint fumes and shit like that. Just don't do it. If you don't have permanent impairment after half a year of abuse, you should count your blessings, not use that as an excuse to keep poisoning yourself.
If you value your life and your health at all, you won't risk throwing it away to get high for a couple hours. Especially when you can get the same high without risking death by using a pure DXM product. CORICIDIN IS TOXIC, and here is the list of fun side effects you can look forward to when your luck runs out and chlorphenamine overdose gets the better of you:
* Dry mouth, eyes, nose, and throat
* A rapid heart rate
* Nausea and vomiting
* Agitation
* Rapid breathing
* Drowsiness
* Dilated pupils
* Flushing
* Fever
* Slowing of the digestive tract
* Low blood pressure
* An irregular heart rhythm
* Confusion
* Hallucinations
* Delirium
* Psychosis
* Seizures
* Coma
* Loss of life.
Sounds like fun, huh?

FFS, wait till tomorrow if everything's closed. If you had no drugs to do besides a nice big bottle of rat poison, would you drink it? Not getting high for one night won't kill you, but CCC abuse might.
By the way, to answer your original question: it will come on faster if you use a brand that doesn't come mixed with a potentially fatal drug that competes for its key metabolic enzyme. In addition to potentially killing you, the chlorphenamine prevents your body from processing the DXM.