Google Docs – How to Insert Special Characters with Keyboard Shortcuts

nhinkle gives the germ of the answer.

Automatic Corrections

Automatic corrections for → and ← are included as defaults. You just need to add your own for ↑ and ↓. (Maybe |^ and |v?)

While editing a document,

1. Select Preferences from the Tools drop-down menu.
2. Either deselect the checkbox next to the word for which you'd like to disable text substitution, or press the "x" to the right of the word to delete the row.

Update 28.02.2016

They seem to have updated the possible keyboard shortcuts. With the new keyboard shortcuts, it also works now on my keyboard with the German layout.

For Windows:

For OS X:

Source: https://support.google.com/docs/answer/179738?hl=en

Original answer

I found a workaround.

1. Select a piece of text in the document.
2. Ctrl+Alt+H opens the Help menu.
3. Arrow down puts the focus in the Search all menus menu.
4. Type "cour", hit Enter.