Hi Max
The musters and paylists will be the most important source as soldiers pay was reduced while they were at sea, as food was provided. Whereas when at home their pay included an amount for buying their own food. It will also include the date he landed. If his record says he served in NSW/Australia for 4 years this includes time at sea. So he is likely to have sailed from Home in 1828. Unfortunately the musters are not on line so you will need a researcher, if the time of your post indicates a location problem.
Most small parties of reinforcements – the main body of the 39th left England in 1825 – would have acted as guards on convict ships. But musters often give the name of the ship for each individual soldier. Failing that their museum may have a copy of their historical records. This should tell you the names of the ships sailing on a particular date. Or you could try online newspaper archives. You need to repeat the process for 1832 when they sailed for India.
I would not recommend visiting Coorg and Gwalior unescorted, due to the risks of crime and dangerous snakes wherever there is long grass. Plus I doubt that the sites will be even signposted. If you google battlefield tours for both Coorg and Gawlior you should get details of local experts. And you should also consider joining fibis.org. They have a forum for asking questions. You should find members who have visited these places.
The 39th Foot became part of the Dorsets, and their museum may have information about guided tours. They probably will not match your timescales, but they may have local contacts in India you can use -
http://www.keepmilitarymuseum.org/For general background you should go on the London Gazette archive and search for the despatches that the General in command would have sent home. These will tell you routes used in the campaigns, plus the names of other regiments brigaded with the 39th Regiment, and are alternative sources. They often give local landmarks, as most campaigns were often a series of skirmishes over many days, rather than a set piece battle on a single day.
Ken
Added... the
Sophia convict ship left Dublin on 7 June 1828 with guards from the 39th Regiment on board. It arrived in NSW on 25 January 1829. There may have been others.