How to win 2 player Pandemic as Quarantine Specialist and Contingency Planner
The contingency planner should ALWAYS have an event card on his character. This frees up cards in his/her hand. It's hard to say whether one or the other should be dedicated to finding cures, it'll most likely depend on who can draw similar colors. The Contingency planner will have a slight advantage in holding cards for cures since both player's event cards can be played then saved on his character card for later use (one at a time obviously).

Quarantine Specialist obviously needs to go where the most cubes are being placed, and would probably be wise to be in charge of erecting research centers to allow quick access to the regions most susceptible to outbreaks.

The tricky dynamic with 2 players is, of course, not wasting cards by having to discard from being over the limit which can often happen when a player is saving for more than 1 cure. So open communication will be critical to prevent those kinds of situations from happening. 

Hope this helps...