I use another image.icns
as my applications icon file.
I've deleted ~/Library/Application Support/NotificationCenter/*.db
and restarted my computer but the notification icon is still the default Mac icon for my application.
Turns out you should probably keep your icons in an ".iconset
". And have all the recommended sizes available for the notification center to pick up (e.g. might be 32 x 32, might be 16 x 16).
And to create this, you can use the "Icon Composer" app to convert your .icns file into a full blown icon set. The .icns file does end up in your built app package / bundle in the end, though.
Details can be found in Apple's "High Resolution Guidelines for OSX" document, under the "Create a set of icons that include high-resolution versions" section.