Geia sou Apowen
I can read greek on my sony prs-600, at least I can read pdf files. I think the fonts have to be embedded for the greek characters to display properly.
Bebook and a device from Plaisio (brand name turbo-x, but most probably re-brand of another device) are sold in Greece, so presumably they support greek characters. I don't think you will have a problem with any device, one way or another. If Greek is not supported natively, you can always embed the greek font or change the default font of the device to one supporting greek.
Now, the availability of greek ebooks is another matter... You can see this post about greek ebooks beginning to appear in the market
https://www.mobileread.com/forums/showthread.php?t=71813. I still can't find any greek ebooks being sold at this moment though... The darknet is a fairly good source until at last the greek ebook market gets going... Oh, and the publisher Kastaniotis does offer some ebooks for free here:
http://www.kastaniotis.com/multimedia/ebooks/
[EDIT] I just tried one of the Kastaniotis epub books and it doesn't work so well. One, I get a "page error" message, which seems to be due to faulty epub construction on their part. But more importantly, they have not embedded any greek font: I could see most characters correctly except for the accented ones... This can be solved however by either embedding a greek font or hacking the device and substituting its default font with another that supports ALL greek characters. Other devices don't need all those workarounds of course. If I remember correctly, cybook had no problems with greek, and even if it did, it gave the user the chance to add fonts without hacking.