For TextMate 2 you can create ~/Library/Application Support/TextMate/KeyBindings.dict
and let it contain something like:
{ "@d" = "showContextMenu:"; }
Here @d
corresponds to ⌘D. See this blog post on how to construct the key equivalent strings.
Source: TextMate mailing list
Key binding files are read in the following order. A new binding for a bound key overrides the previous one:
/System/Library/Frameworks/AppKit.framework/Resources/StandardKeyBinding.dict
/Library/KeyBindings/DefaultKeyBinding.dict
~/Library/KeyBindings/DefaultKeyBinding.dict
/path/to/TextMate.app/Contents/Resources/KeyBindings.dict
~/Library/Application Support/TextMate/KeyBindings.dict
A relaunch of TextMate (⌃⌘Q) is required before changes take effect.