ß isn't beta. It's the (german) sharp s. The greek beta looks like this: β.
The fastest method probably is:
- enable the greek keyboard layout permamently in System Preferences -> Keyboard -> Input Sources
- defining and enabling a free keyboard shortcut in System Preferences -> Keyboard -> Shortcuts -> Input Sources -> Select next source in input menu (e.g ShiftAltSpacebar)
To type α/β/γ/ε etc., you just have to switch the keyboard layout with ShiftAltSpacebar, hit A/B/G/E etc. and switch back to your common keyboard layout with ShiftAltSpacebar. If you have more than two keyboard layouts enabled (e.g. US, Greek, Hex) you may add a second keyboard shortcut "Select previous source in input menu" and hit that one to get back or you have to rotate through all your layouts with the "Select next source in input menu"-shortcut until you reach your common layout again.
Karabiner/KeyRemap4MacBook offer a remapping of the right Option/alt key to temporarily switch to the greek keyboard layout in the presets (the greek keyboard layout has to be enabled):
In Lion this doesn't work properly and interferes with Spotlight. I had to turn off the Spotlight shortcuts in System Preferences -> Keyboard -> Shortcuts -> Spotlight. One might add a customized remapping by modifying a copy of the original source to get it working without disabling the Spotlight shortcuts:
<name>Change input source temporary</name>
<name>Change input source to Greek while you are holding down right option key.</name>
Option::KEYTOKEY_BEFORE_KEYDOWN, KeyCode::VK_CHANGE_INPUTSOURCE_GREEK, KeyCode::VK_WAIT_100MS,
Option::KEYTOKEY_AFTER_KEYUP, KeyCode::SPACE, ModifierFlag::OPTION_L, ModifierFlag::SHIFT_L, KeyCode::VK_WAIT_100MS,