Met de trein naar Kalamata:

Treintijden Athene - Kalamata http://www.athensguide.com/practicalinfo/suburban-railway.htm

Je kunt eventueel per trein vanuit Athene naar de Peloponessos. Er is een treinverbinding van Korinthe-Patras-Pirgos-Olympia-Kalamata-Tripoli-Nafplio-Korinthe en veel tussenliggende dorpen.
De reis duurt erg lang en wordt niet aangeraden.

Volgens de laatste informatie eindigt de reis in Tripoli, wegens reorganistie van de treinverbinding (i.v.m. het nieuwe traject van de snelweg A7)

Er is GEEN directe verbinding van Athene naar Kalamata.

There is NO direct service from Athens Airport to Kalamata.

You must take the BUS in to the downtown main Athens station (SYNTAGMA).
There you take the METRO to Korinth.

Trains leave for Kalamata at 06:06, 12:06, 15:06 and 23:06 daily.
It takes about 7 hours.
Ticket price 13 euro / 19:20 euro (IC)

Attention
Bus is your best option by far, the only train that comes into Kalamata is the one that goes all the way round the west coast of the Peloponnese, takes about 6 hours just from Corinth!

It's more than 7 hours by train from Athens to Kalamata with a change in Kiato, that's assuming your trains run on time.

Another alternative would be to fly. Aegean has direct flights twice a day and prices are very reasonable: 47€ each way for a saver fare.
The flight is just a short 45 min hop.
See page:
Flights
Vliegtickets

links:
http://www.virtualtourist.com/
http://www.youtube.com/watch?v=MsTnf_c5foE
http://en.wikipedia.org/wiki/Piraeus,_Athens_and_Peloponnese_Railways
http://en.wikipedia.org/wiki/File:Greek_railway_network.svg
http://www.tripadvisor.com/ShowTopic-g189483-i1277-k3588755-l25855144-Train_travel_from_Korinth_to_Kalamata-Peloponnese.html