I used Automator to make a Service workflow, and Keyboard System Preferences to give it a combo keystroke. Text-replacement wasn't introduced until 10.13 High Sierra, and this was the best single-keystroke method I found for such versions (tested on 10.6 Snow Leopard).
First open Applications >> Automator, choose the "Service" template, set "Service recieves" to "no input", enable "Replaces selected text", doubleclick the "Run Applescript" action, replace its contents with the following:
on run {}
return (character id 945)
end run
and Save it with your desired name (e.g., "α", "Paste an alpha character", etc.).
Then open System Preferences >> Keyboard >> Keyboard Shortcuts >> Services, scroll down to Text services, find your new one, click somewhere in the empty white space to the farthest right of its name, and when the text entry box appears, press your desired key combo (I used command-option-shift-A).
The only downsides are that it leaves the character selected, so you have to deselect it (right-cursor, mouse click, etc.) before entering more text (which I guess makes it 2 keystrokes), and it's slow, takes about a second.