SQL Server 2008 Script Changes from Database Diagram
More Google searching did not help, but after fiddling around with SSMS I managed to figure it out. Thought I'd answer my own question for anyone else who might stumble across this.

To script all of the changes at once, simply right-click a blank area of the diagram and click 'Select All' (or press Ctrl+A). Then right-click one of the selected tables and choose 'Generate Change Script...' at the bottom.