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llLocalInstantMessage(key id, string message);
Exactly the same as the current llInstantMessage() feature, except that this one works locally, if the specified ID is not present in the simulator then the request is ignored. This function only has a short delay (since it is now basically a focused llSay function).
Additionally, this function could also be used to IM objects in the same simulator, immediately calling any relevant listen() events in the object with a channel of zero (thus to test an IM received you just check for channel zero in an object that does not listen to them). No listen would be required for this however since the IM is direct.
Implementation-wise it probably wouldn't be an IM at all, but in behaviour it is the same minus out-of-sim communications capabilities.
It just seems pointless to have to place 10 or more instant messenger scripts in an object just to send messages to someone interacting with my object without spamming everyone else nearby.