First of of all, there is no railway station in Coorg

First of of all, there is no railway station in Coorg. The nearest practical railway station is Mysore Junction (Station code: MYS).

So, essentially you'll be traveling from Chennai to Mysore by train and from Mysore to Coorg by road.

The Chennai to Coorg route is like this: Chennai -> Bangalore -> Mysore -> Madikeri (or any other place in Coorg)

Let's first talk about the Chennai to Mysore Train options. There are two daily express trains between Mysore and Chennai. Kaveri Express from Chennai Central (Station Code : MAA) is overnight train from Chennai to Mysore (Train No: 16222 , return Train No: 16221).

Shatabdi Express is the second main option. It's a day traveling train , fast (only 1 stop at Bangalore, between Chennai and Mysore) and expensive too. Train Number 12007 travels to Mysore from Chennai and Train No:12008 is the return Shatabdi Express.

Additionally there are 2 more weekly trains that connects Chennai with Mysore , Bagmati Express (Train Number :12577) and the Mysore Express (Train Number : 22682).

Kaveri Express takes about 10+ hours while Shatabdi Express covers it it about 7 hours time.

A sleeper ticket costs about Rs300 in Kaveri Express and AC Chair Car about Rs1000 in Shatabdi Express. Of course there are many other classes too.

Check the schedules and book the tickets well in advance ( There are are pretty crowded trains where reservations get filled fast.

That's about Chennai to Mysore stretch of the journey to Coorg. From Mysore take one of those buses (KSRTC) to Coorg. There are frequent services to Madikeri and also other towns in Coorg.

Another option is to hire a cab to Coorg from Mysore.