Oh, that!
You need to implement a UITypeEditor, which can provide either a popup or a
drop-down (both drawing whatever you want). If fixed drop-down (text) lists
and text editing / parsing are what you want, then you also need to look at
TypeConverter.
See MSDN:
http://msdn2.microsoft.com/en-us/library/ms171840.aspx
(note that although you can support painting a preview in the grid, you
can't really put a button there until the user selects the drop-down; think
of the Dock /Anchor propertes for forms and you'll get the picture).
Note that this aspect of the component model can take some time to
understand, but it is very powerful.
Marc