You can't do this without a nasty hacks - there's no API for this, no way to notify the process that its environment has changed (since that's not really possible anyway).
Even if you do manage to do that, there is no way to be sure that it will have any effect - the process could very well have cached the environment variable you're trying to poke (since nothing is supposed to be able to change it).
If you really do want to do this, and are prepared to pick up the pieces if things go wrong, you can use a debugger. See for instance this Stack Overflow question:
Is there a way to change another process's environment variables?
(gdb) attach process_id
(gdb) call putenv ("DISPLAY=your.new:value")
Other possible functions you could try to call are
Please do really keep in mind that this may not work, or have dire consequences if the process you target does "interesting" things with its environment block. Do test it out on non-critical processes first, but make sure these test processes mirror as close as possible the one you're trying to poke.