Being a person who have lived in coorg for years I would suggest take a flight preferably to kannur and then you get buses to coorg. Else the nearest option next is mysore but the flight connectivity might be issue. Next option. Is mangalore of course and get a bus to madikeri but its for sure 3 hours plus travel.
No, nearest airports are Bangalore & Kannur. Mysore airport operates only Chennai routes so road is the best option from Bangalore, Kannur or Mangalore airports.
There is no direct flight from Pune to Coorg, You need to.take flight From Pune to Mysore or Mangalore Airport which is around 120 to 150 Km from Coorg.