The journey from Gangtok to Coimbatore covers roughly 2600 km. You must first reach NJP or Bagdogra. From NJP, you can take a long-distance train to Coimbatore Junction. Flights from Bagdogra to Coimbatore usually connect through Bangalore or Chennai.
Total Distance: 2600 km by road, 2100 km air distance.
This is a very long journey; ensure you have a confirmed berth.
Bangalore is the most convenient hub for this connection.
October to March for pleasant weather.