Here's what I did:
I fired up my eMac, checked for SPIonic font, and verified it wasn't available yet on that system.
I started Safari, looked at a textkit thread with spionic: I saw betacode, no Greek characters.
I then downloaded the SPIonic font from the Monachos site, unstuffed the downloaded sit file and placed the font on my desktop.
I double clicked the font, Fontbook opened, and I clicked on Install.
The font was installed to my Library/Fonts folder (User, not the System Library folder, but it shouldn't make a difference).
I quit Safari and started it again, to take a look at the same thread as before: now I could see Greek characters.
Can you describe, step by step, what you did to install the font? It must be something really tiny that we are overlooking.
Otherwise I will help you find those Ancient Greek swear words