It is important to note that in order to solo old raid content, you need gear that can only be acquired in groups and raids.
So you have to spend years grouping and raiding in order to solo Trakanon. Very anticlimatic. If you are CoA geared with 1200 AAs and can't solo Trak, you are a loser.
To answer the original question...
No. No classes can solo a Dragon.
If you start Everquest now and solo your way to level 70 and 1200 AAs without raiding and getting raid gear, you will not be able to solo dragons.
I doubt very much a purely LDoN, DoN or MPG Trial geared player can solo a dragon. Even if they can, LDoN DoN and MPG trials all require groups (or multi boxing) and cannot be soloed either.
Edited, Wed Jan 18 21:04:05 2006 by Reyla
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After 16 years, I'm not listing every friggin character.