Avoidance …
Overtraining, probably increases the chances of illness the greatest, specifically longer endurnace work or greater volumes due to parasympathetic activiation and suppressed immune response. This coupled with lowered bodyfat after a pre-season certainly leads to greater likelihood of colds & flu.
The only way I know possible to avoid it is using an Omegawave, but they are incredibly expensive, time consuming and not many are willing to invest.
Recovery …
Rest is paramount, but some training specific to the type of illness is possible and certainly effective in encouraging the body to respond. Vitamin C, Zinc, Ginger, Garlic & Lemon are all helpful also.
Timing
It may also be well worth looking at the timing of a cold and it’s appearance as you have some control over when it hits … if you know it’s coming (with OW or symptoms) you can speed up it’s arrival or delay it to just avoid major games. It is also possible to have a great performance just before it hits big time as the body, by mobilising defences and the CNS can allow greater energy expenditures … of course in the days post game the player is usually knocked for six. The Russians used these techniques in Olympic games with athletes.