SuperToast and m.r.bob have the right ideas there. I think you have already found out that the Archon beam is a separate GRP file from the main Archon, but it is linked to the Archon through iscript. The basic jist of what you'd have to do is you'd need to re-add the beam to images.dat and the MPQ as a separate image, possibly changing images.tbl in the process. I don't think it's that hard, but I have been doing this a while, so I might be out of touch with how hard it really is.
For this, you need Arsenal Zero because Arsenal III corrupts arr\images.dat each time it edits it.
1. Find the ID of the Archon beam in images.dat. The easiest way to do this is to extract the Archon's iscript and look for the image overlay command in its attack animation which will be creating the beam. Memorise this ID number, or make a note of it somewhere. We will be copying all the details of this images.dat entry to your new images.dat entry.
2. Extract the archon beam GRP file (you can get it's filename from the iscript you just extracted) from the MPQ, edit it to be red and resave it to a GRP file using RetroGRP. Now add the edited red beam GRP file to the MPQ. Use whatever filename you like, as long as it starts with "unit\". For example, "unit\protoss\myredbeam.grp".
3. Extract a fresh copy of arr\images.tbl from the MPQ. Edit it with TblPad. In here are all the filenames of all the GRPs in StarCraft, without "unit\" at the start, as StarCraft assumes they all will start with "unit\". Add your filename right down the bottom, without the "unit\" part. For example, add "protoss\myredbeam.grp" to the bottom of images.tbl. Look in the title bar and memorise the ID number of your new images.tbl entry. We will need to give this to a new images.dat entry so that it points to your new GRP file.
4. Using Arsenal Zero, convert your images.dat file into an INI file, which I assume will be called images.txt. If you open it up you'll see a whole lot of entries
CODE
[0:Scourge]
(all sorts of properties for this image...)
[1:Scourge Shadow]
(I'm just listing these off the top of my head, so they're more than likely to be wrong...)
The nice thing about the headings is they all start with their ID numbers. So, jump to the ID number of the archon beam by searching for "(id number):". For example, if you found the Archon Beam's image ID to be 443, then search for "443:" and you'd jump straight to that entry. Copy everything about the Archon Beam.
5. Now, search for an unused images.dat entry, you can find those by searching for "unused". You'll jump straight to an entry like "[373:Protoss Scout (Unused)]" (it won't look like that though). Overwrite all the properties of this entry with the properties of the original Archon beam that you copied from step 4. You now have two blue Archon beam entries. Memorise the images.dat ID of this second entry that you're about to change.
6. All you need to do now is change your duplicate blue Archon beam into your red one. To do that, change the "File" property to the images.tbl ID of your new GRP file. You memorised this in step 3. Now I can't remember exactly whether TblPad counts images.tbl IDs starting from 0 or 1, if it counts starting from 1 you'd need to make this ID one less, because StarCraft counts from 0. Notice that the iscripts for the two beams are the same. That's the easiest way to do it, since the graphics will have the same frames anyway, it sounds appropriate.
7. Now, open the iscript for the Dark Archon using ICE or IceCC, find its attack animation, go to the line where it does its image overlay (imgol08 or whatever the command is for this situation) and change the images.dat ID it uses to the one you memorised in step 5.
Now, whenever your Dark Archon attacks, it will use your new images.dat ID, which will use your new images.tbl ID, which will use your new GRP file. Ta da! It's quite logical to me, I think you could definitely do it. Try it out.